[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-572343-105":53,"doc-detail-572343-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","polar-coordinates-cheat-sheet-maple-software-reference","Polar Coordinates Cheat Sheet - Maple Software Reference","","This document serves as a mathematical cheat sheet for plotting common curves in polar coordinates using the Maple software environment. It covers the syntax and functional definitions for generating circles, straight lines, and cardioids. Each section provides specific code examples, demonstrating how to define radius functions in terms of theta using trigonometric identities like sine, cosine, secant, and cosecant. The guide is intended as a quick-reference resource for students and practitioners utilizing computer algebra systems for coordinate geometry visualization.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/polar-coordinates-cheat-sheet-maple-software-reference/572343/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/polar-coordinates-cheat-sheet-maple-software-reference/572343.png","ImageObject",442,249,{"name":88,"@type":89},"Valentina","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-20","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":79},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"How do you define a circle in polar coordinates using Maple?","Question",{"text":108,"@type":109},"Circles are defined by setting the radius function to a constant, such as r := theta -> a, where 'a' represents the constant radius.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"What is the general form of a cardioid as presented in the sheet?",{"text":113,"@type":109},"Cardioids are defined using the form r = a +/- a*sin(theta) or r = a +/- a*cos(theta), where 'a' is a scaling constant.",{"name":115,"@type":106,"acceptedAnswer":116},"How are vertical and horizontal lines represented in this polar coordinate guide?",{"text":117,"@type":109},"Lines are represented using trigonometric functions, specifically r = a*sec(theta) for vertical lines and r = a*csc(theta) for horizontal lines.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},572343,1792014119,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":79,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":135,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":141},13056703020460,"https://ap-avatar.wpscdn.com/avatar/be000253dac470eee5d?_k=1778207105932848923","> restart:  \n> with (student):with(plots):  \nWarning, the name changecoords has been redefined  \nI. Circles  \n> a:=1;  \na := 1  \n> r:= theta -> a;plot([r(theta),theta,theta= 0 . .2*Pi],coords=polar);  \nr := θ → a  \n> r:= theta -> a* sin(theta);plot([r(theta),theta,theta= 0 . .2*Pi],coords=polar);  \nr := θ → a sin( θ )  \n> r:= theta -> -a* sin(theta);plot([r(theta),theta,theta= 0 . .2*Pi],coords=polar);  \nr := θ → −a sin( θ )  \n> r:= theta -> a* cos(theta);plot([r(theta),theta,theta= 0 . .2*Pi],coords=polar);  \nr := θ → a cos( θ )  \n> r:= theta -> -a* cos(theta);plot([r(theta),theta,theta= 0 . .2*Pi],coords=polar);  \nr := θ → −a cos( θ )  \nII Lines  \n> a:=1;  \na := 1  \n> r:= theta -> a*sec(theta);plot([r(theta),theta,theta= 0 . .2*Pi],coords=polar);  \nr := θ → a sec( θ )  \n> r:= theta -> -a* sec(theta);plot([r(theta),theta,theta= 0 . .2*Pi],coords=polar);  \nr := θ → −a sec( θ )  \n> r:= theta -> a* csc(theta);plot([r(theta),theta,theta= 0 . .2*Pi],coords=polar);  \nr := θ → a csc( θ )  \n> r:= theta -> -a* csc(theta);plot([r(theta),theta,theta= 0 . .2*Pi],coords=polar);  \nr := θ → −a csc( θ )  \nIII  \nCardiods: { Form r = a +/-a sin(theta) or r = a +/-cos(theta)  \n> a:=1;  \na := 1  \n> r:= theta -> a + a*sin(theta);plot([r(theta),theta,theta= 0 . .2*Pi],coords=polar);  \nr := θ → a + a sin( θ )  \n> r:= theta -> a -a*sin(theta);plot([r(theta),theta,theta= 0 . .2*Pi],coords=polar);  \nr := θ → a − a sin( θ )","cbCaimVfAiFwnvHl","https://ap.wps.com/l/cbCaimVfAiFwnvHl","pdf",273212,23,"English","# I. Circles\n# II. Lines\n# III. Cardiods","[{\"question\":\"How do you define a circle in polar coordinates using Maple?\",\"answer\":\"Circles are defined by setting the radius function to a constant, such as r := theta -\\u003e a, where 'a' represents the constant radius.\"},{\"question\":\"What is the general form of a cardioid as presented in the sheet?\",\"answer\":\"Cardioids are defined using the form r = a +/- a*sin(theta) or r = a +/- a*cos(theta), where 'a' is a scaling constant.\"},{\"question\":\"How are vertical and horizontal lines represented in this polar coordinate guide?\",\"answer\":\"Lines are represented using trigonometric functions, specifically r = a*sec(theta) for vertical lines and r = a*csc(theta) for horizontal lines.\"}]","Polar Coordinates Cheat Sheet - Maple Software Reference | PDF",1791926853,8]