{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":336,"title":"Similar Triangles - find the height of the tree","description":"Given the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\r\n\r\n\r\nInputs: h1, x1, x2\r\n\r\nOutput: h2\r\n\r\nHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\r\n\r\nEX:\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\r\n\r\n\u003e\u003eh2=findHeight(x1,x2,h1)\r\n\r\nh2=6\r\n\r\n\u003e\u003e","description_html":"\u003cp\u003eGiven the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\u003c/p\u003e\u003cp\u003eInputs: h1, x1, x2\u003c/p\u003e\u003cp\u003eOutput: h2\u003c/p\u003e\u003cp\u003eHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\u003c/p\u003e\u003cp\u003eEX:\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\u003c/p\u003e\u003cp\u003e\u003e\u003eh2=findHeight(x1,x2,h1)\u003c/p\u003e\u003cp\u003eh2=6\u003c/p\u003e\u003cp\u003e\u003e\u003e\u003c/p\u003e","function_template":"function h2 = findHeight(x1,x2,h1)\r\n  h2 = heightoftree\r\nend","test_suite":"%%\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\r\ny_correct = 6;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 8;\r\nh1 = 3;\r\ny_correct = 9;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 12;\r\nh1 = 3;\r\ny_correct = 12;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 16;\r\nh1 = 3;\r\ny_correct = 15;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 20;\r\nh1 = 3;\r\ny_correct = 18;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 24;\r\nh1 = 3;\r\ny_correct = 21;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 12;\r\nh1 = 5;\r\ny_correct = 20;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 16;\r\nh1 = 10;\r\ny_correct = 50;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 2;\r\nx2 = 4;\r\nh1 = 5;\r\ny_correct = 15;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 3;\r\nx2 = 6;\r\nh1 = 4;\r\ny_correct = 12;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":6,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":470,"test_suite_updated_at":"2012-02-18T04:42:47.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-02-17T22:52:21.000Z","updated_at":"2026-04-08T05:02:48.000Z","published_at":"2012-02-18T04:42:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs: h1, x1, x2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: h2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEX: x1 = 4; x2 = 4; h1 = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003e\u003eh2=findHeight(x1,x2,h1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eh2=6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003e\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":837,"title":"Find all the zeros of sinus , cosinus and tangent in a given interval","description":"The aim is to find all the zeros of a function within an interval.\r\n\r\n*Input* : \r\n\r\n* fcn : an anonymous function (@sin, @cos...)\r\n* \r\n* lb : lower bound\r\n* \r\n* ub :upper bound\r\n\r\n\r\n*Output* :\r\n\r\n* output :  vector with unique values for which the input function return zero\r\nThe values must be sorted in ascending order. \r\n\r\n*Example* \r\n\r\n\r\n\r\n  output = find_zeros(@sin,0,2*pi) will return :\r\n\r\n  output = [0.0000    3.1416    6.2832]\r\n\r\nsince the sinus function between [0 2pi] is zero for [0 pi 2pi]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 197px; vertical-align: baseline; perspective-origin: 332px 197px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe aim is to find all the zeros of a function within an interval.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eInput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-bottom: 20px; margin-top: 10px; transform-origin: 316px 50px; perspective-origin: 316px 50px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efcn : an anonymous function (@sin, @cos...)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elb : lower bound\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eub :upper bound\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eOutput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-bottom: 20px; margin-top: 10px; transform-origin: 316px 20px; perspective-origin: 316px 20px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 20px; white-space: pre-wrap; perspective-origin: 288px 20px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eoutput : vector with unique values for which the input function return zeroThe values must be sorted in ascending order.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003eoutput = find_zeros(@sin,0,2*pi) will \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003ereturn :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003eoutput = [0.0000    3.1416    6.2832]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003esince the sinus function between [0 2pi] is zero for [0 pi 2pi]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function output = find_zeros(fcn,lb,ub)\r\noutput = lb*up;","test_suite":"%% Test sinus between [0 2pi]\r\nassert(all(abs(find_zeros(@sin,0,2*pi) -[0 pi 2*pi])\u003c1e-9))\r\n\r\n%% [0 pi]\r\nassert(all(abs(find_zeros(@sin,0,pi) -[0 pi ])\u003c1e-9))\r\n\r\n%% [0 pi/3] \r\nassert(all(abs(find_zeros(@sin,0,pi/3) -0) \u003c1e-9))\r\n\r\n%% Test cos between [0 2pi]\r\nassert(all(abs(find_zeros(@cos,0,2*pi) -[pi/2 3*pi/2])\u003c1e-9))\r\n\r\n%% Test tan between [0 pi/4]\r\nassert(all(abs(find_zeros(@tan,0,pi/4) -0)\u003c1e-9))","published":true,"deleted":false,"likes_count":1,"comments_count":7,"created_by":639,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":"2020-09-29T14:30:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-17T07:42:46.000Z","updated_at":"2026-01-03T12:33:06.000Z","published_at":"2012-07-17T08:10:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe aim is to find all the zeros of a function within an interval.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efcn : an anonymous function (@sin, @cos...)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elb : lower bound\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eub :upper bound\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput : vector with unique values for which the input function return zeroThe values must be sorted in ascending order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[output = find_zeros(@sin,0,2*pi) will return :\\n\\noutput = [0.0000    3.1416    6.2832]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esince the sinus function between [0 2pi] is zero for [0 pi 2pi]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":336,"title":"Similar Triangles - find the height of the tree","description":"Given the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\r\n\r\n\r\nInputs: h1, x1, x2\r\n\r\nOutput: h2\r\n\r\nHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\r\n\r\nEX:\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\r\n\r\n\u003e\u003eh2=findHeight(x1,x2,h1)\r\n\r\nh2=6\r\n\r\n\u003e\u003e","description_html":"\u003cp\u003eGiven the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\u003c/p\u003e\u003cp\u003eInputs: h1, x1, x2\u003c/p\u003e\u003cp\u003eOutput: h2\u003c/p\u003e\u003cp\u003eHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\u003c/p\u003e\u003cp\u003eEX:\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\u003c/p\u003e\u003cp\u003e\u003e\u003eh2=findHeight(x1,x2,h1)\u003c/p\u003e\u003cp\u003eh2=6\u003c/p\u003e\u003cp\u003e\u003e\u003e\u003c/p\u003e","function_template":"function h2 = findHeight(x1,x2,h1)\r\n  h2 = heightoftree\r\nend","test_suite":"%%\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\r\ny_correct = 6;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 8;\r\nh1 = 3;\r\ny_correct = 9;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 12;\r\nh1 = 3;\r\ny_correct = 12;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 16;\r\nh1 = 3;\r\ny_correct = 15;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 20;\r\nh1 = 3;\r\ny_correct = 18;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 24;\r\nh1 = 3;\r\ny_correct = 21;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 12;\r\nh1 = 5;\r\ny_correct = 20;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 16;\r\nh1 = 10;\r\ny_correct = 50;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 2;\r\nx2 = 4;\r\nh1 = 5;\r\ny_correct = 15;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 3;\r\nx2 = 6;\r\nh1 = 4;\r\ny_correct = 12;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":6,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":470,"test_suite_updated_at":"2012-02-18T04:42:47.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-02-17T22:52:21.000Z","updated_at":"2026-04-08T05:02:48.000Z","published_at":"2012-02-18T04:42:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs: h1, x1, x2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: h2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEX: x1 = 4; x2 = 4; h1 = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003e\u003eh2=findHeight(x1,x2,h1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eh2=6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003e\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":837,"title":"Find all the zeros of sinus , cosinus and tangent in a given interval","description":"The aim is to find all the zeros of a function within an interval.\r\n\r\n*Input* : \r\n\r\n* fcn : an anonymous function (@sin, @cos...)\r\n* \r\n* lb : lower bound\r\n* \r\n* ub :upper bound\r\n\r\n\r\n*Output* :\r\n\r\n* output :  vector with unique values for which the input function return zero\r\nThe values must be sorted in ascending order. \r\n\r\n*Example* \r\n\r\n\r\n\r\n  output = find_zeros(@sin,0,2*pi) will return :\r\n\r\n  output = [0.0000    3.1416    6.2832]\r\n\r\nsince the sinus function between [0 2pi] is zero for [0 pi 2pi]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 197px; vertical-align: baseline; perspective-origin: 332px 197px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe aim is to find all the zeros of a function within an interval.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eInput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-bottom: 20px; margin-top: 10px; transform-origin: 316px 50px; perspective-origin: 316px 50px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efcn : an anonymous function (@sin, @cos...)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elb : lower bound\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eub :upper bound\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eOutput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-bottom: 20px; margin-top: 10px; transform-origin: 316px 20px; perspective-origin: 316px 20px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 20px; white-space: pre-wrap; perspective-origin: 288px 20px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eoutput : vector with unique values for which the input function return zeroThe values must be sorted in ascending order.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003eoutput = find_zeros(@sin,0,2*pi) will \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003ereturn :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003eoutput = [0.0000    3.1416    6.2832]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003esince the sinus function between [0 2pi] is zero for [0 pi 2pi]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function output = find_zeros(fcn,lb,ub)\r\noutput = lb*up;","test_suite":"%% Test sinus between [0 2pi]\r\nassert(all(abs(find_zeros(@sin,0,2*pi) -[0 pi 2*pi])\u003c1e-9))\r\n\r\n%% [0 pi]\r\nassert(all(abs(find_zeros(@sin,0,pi) -[0 pi ])\u003c1e-9))\r\n\r\n%% [0 pi/3] \r\nassert(all(abs(find_zeros(@sin,0,pi/3) -0) \u003c1e-9))\r\n\r\n%% Test cos between [0 2pi]\r\nassert(all(abs(find_zeros(@cos,0,2*pi) -[pi/2 3*pi/2])\u003c1e-9))\r\n\r\n%% Test tan between [0 pi/4]\r\nassert(all(abs(find_zeros(@tan,0,pi/4) -0)\u003c1e-9))","published":true,"deleted":false,"likes_count":1,"comments_count":7,"created_by":639,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":"2020-09-29T14:30:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-17T07:42:46.000Z","updated_at":"2026-01-03T12:33:06.000Z","published_at":"2012-07-17T08:10:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe aim is to find all the zeros of a function within an interval.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efcn : an anonymous function (@sin, @cos...)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elb : lower bound\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eub :upper bound\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput : vector with unique values for which the input function return zeroThe values must be sorted in ascending order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[output = find_zeros(@sin,0,2*pi) will return :\\n\\noutput = [0.0000    3.1416    6.2832]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esince the sinus function between [0 2pi] is zero for [0 pi 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