[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523537-105":59,"doc-detail-523537-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","infinite-precalculus-parametric-equations-worksheet-05-parametric-equations","Infinite Precalculus Parametric Equations - Worksheet 05 - Parametric Equations","","Infinite Precalculus parametric-equations worksheet focused on sketching and converting between parametric and rectangular forms. Students complete problems by graphing the curve for given pairs of parametric equations, then rewrite each pair in rectangular form. Additional items use the parameter to convert rectangular equations back into parametric form, followed by critical thinking questions requiring alternate parameterizations that represent the same function with slower or faster speed and possibly opposite orientation.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/infinite-precalculus-parametric-equations-worksheet-05-parametric-equations/523537/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/infinite-precalculus-parametric-equations-worksheet-05-parametric-equations/523537.png","ImageObject",300,407,{"name":92,"@type":93},"LangkahRina","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What do the problems ask students to do first?","Question",{"text":113,"@type":114},"Sketch the curve for each given pair of parametric equations.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do students complete the next set of questions?",{"text":118,"@type":114},"Rewrite each pair of parametric equations in rectangular form.",{"name":120,"@type":111,"acceptedAnswer":121},"What is required for the critical thinking questions?",{"text":122,"@type":114},"Write two parametric representations of the same function, then modify the speed (slower/faster) and, for one question, use an opposite orientation.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},523537,1791512717,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":52,"preview_page_count":4},962090893776,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Kuta Software-Infinite Precalculus Parametric Equations  \nSketch the curve for each pair of parametric equations.  \nName  Date  Period   \n1) x 􀀠 t, y 􀀠 ~~ ~~t~~ ~~􀀕􀀗~~ ~~  \n3) x 􀀠 􀀘 sin t, y 􀀠 􀀗 cos t  \n2) x 􀀠 􀀐􀀕 t 􀀎 􀀕 , y 􀀠 􀀗t􀀘􀀕 􀀐 􀀕 , 􀀐􀀕 􀁤 t 􀁤 􀀖  \n4) x 􀀠 􀀕 sec t, y 􀀠 􀀗tan t  \nWrite each pair of parametric equations in rectangular form.  \n5) x 􀀠 􀀐 ~~ ~~t~~ ~~􀀕􀀖~~ ~~, y 􀀠 t 6) x 􀀠 t, y 􀀠 ~~ ~~t~~ ~~􀀕􀀙 􀀎 􀀕􀀖t 􀀐 ~~ ~~􀀔􀀖~~ ~~  \n7) x 􀀠 􀀐􀀕 t 􀀐 􀀖 , y 􀀠 􀀕 t􀀕 􀀎 􀀕 t 􀀐 􀀘􀀕~~ ~~ 8) x 􀀠 􀀕sin t, y 􀀠 􀀗 cos t  \n9) x 􀀠 sec t, y 􀀠 􀀗tan t 10) x 􀀠 􀀗 cos t 􀀐 􀀔 , y 􀀠 􀀖sin t 􀀎 􀀔  \nUse the parameter to write each rectangular equation as a pair of parametric equations.  \n11) x 􀀠 y􀀕􀀙~~ ~~, t 􀀠 y 12) y 􀀠 􀀐 ~~ ~~x􀀕􀀗 􀀎 x 􀀎 􀀔 , t 􀀠 􀀐 ~~ ~~ 􀀎 ~~ ~~􀀔􀀖~~ ~~  \nCritical thinking questions:  \n13) Write a set of parametric equations that represent y 􀀠 x 􀀕 􀀐 􀀗x. Then write a second set of parametric equations that represent the same function, but with a slower speed  \n14) Write a set of parametric equations that represent y 􀀠 x 􀀕 􀀐 􀀔 . Then write a second set of parametric equations that represent the same function, but with a faster speed and an opposite orientation.  \nKuta Software-Infinite Precalculus Parametric Equations  \nSketch the curve for each pair of parametric equations.  \nName  Date  Period   \n1) x 􀀠 t, y 􀀠 ~~ ~~t~~ ~~􀀕􀀗~~ ~~  \n3) x 􀀠 􀀘 sin t, y 􀀠 􀀗 cos t  \n2) x 􀀠 􀀐􀀕 t 􀀎 􀀕 , y 􀀠 􀀗t􀀘􀀕 􀀐 􀀕 , 􀀐􀀕 􀁤 t 􀁤 􀀖  \n4) x 􀀠 􀀕 sec t, y 􀀠 􀀗tan t  \nWrite each pair of parametric equations in rectangular form.  \n5) x 􀀠 􀀐 ~~ ~~t~~ ~~􀀕􀀖~~ ~~, y 􀀠 t  \n􀀕  \ny x 􀀠 􀀐  􀀖   \n7) x 􀀠 􀀐􀀕 t 􀀐 􀀖 , y 􀀠 􀀕 t􀀕 􀀎 􀀕 t 􀀐 􀀘􀀕~~ ~~  \ny 􀀠 x􀀕􀀕 􀀎 􀀕x 􀀐 􀀔  \n9) x 􀀠 sec t, y 􀀠 􀀗tan t  \n􀀕  \nx 􀀐  \n􀀕  \ny   \n􀀔􀀙  \n􀀠 􀀔  \n6) x 􀀠 t, y 􀀠 ~~ ~~t~~ ~~􀀕􀀙 􀀎 􀀕􀀖t 􀀐 ~~ ~~􀀔􀀖~~ ~~  \ny 􀀠  \n􀀕  \nx  \n􀀙  \n􀀎  \n 􀀕x   􀀔   \n􀀐  \n􀀖 􀀖  \n8) x 􀀠 􀀕sin t, y 􀀠 􀀗 cos t  \n~~ ~~x~~ ~~􀀕􀀗 􀀎 ~~ ~~y􀀔􀀕􀀙~~ ~~ 􀀠 􀀔  \n10) x 􀀠 􀀗 cos t 􀀐 􀀔 , y 􀀠 􀀖sin t 􀀎 􀀔  \n~~ ~~(x~~ ~~􀀔)􀀕 􀀎 ~~ ~~(y~~ ~~~~ ~~􀀔)􀀕 􀀠 􀀔  \nUse the parameter to write each rectangular equation as a pair of parametric equations.  \n11)  \nx 􀀠  \n􀀕  \ny   \n􀀙 ,  \nx 􀀠  \nt􀀕  \n􀀙 ,  \nt 􀀠 y  \ny 􀀠 t  \n12) y 􀀠 􀀐 ~~ ~~x􀀕􀀗 􀀎 x 􀀎 􀀔 , t 􀀠 􀀐 ~~ ~~ 􀀎 ~~ ~~􀀔􀀖~~ ~~  \nx 􀀠 􀀐􀀖 t 􀀎 􀀔 , y 􀀠 􀀐 ~~ ~~􀀜􀀕 􀀐 ~~ ~~􀀖􀀕t 􀀎 􀀚􀀗~~ ~~  \nCritical thinking questions:  \n13) Write a set of parametric equations that represent y 􀀠 x 􀀕 􀀐 􀀗x. Then write a second set of parametric equations that represent the same function, but with a slower speed  \nMany answers. Ex: y 􀀠 t􀀕 􀀐 􀀗 t, x 􀀠 t and y 􀀠 ~~ ~~t~~ ~~􀀕􀀗 􀀐 􀀕 t, x 􀀠   \n14) Write a set of parametric equations that represent y 􀀠 x 􀀕 􀀐 􀀔 . Then write a second set of parametric equations that represent the same function, but with a faster speed and an opposite orientation.  \nMany answers. Ex: y 􀀠 t􀀕 􀀐 􀀔 , x 􀀠 t and y 􀀠 􀀗 t􀀕 􀀐 􀀔 , x 􀀠 􀀐􀀕 t  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaij8klLwbEfoe","https://ap.wps.com/l/cbCaij8klLwbEfoe","pdf",51226,"English","# Sketch the Curve\n## Convert Between Parametric and Rectangular Form\n## Use the Parameter for Rectangular Equations\n## Critical Thinking Questions","[{\"question\":\"What do the problems ask students to do first?\",\"answer\":\"Sketch the curve for each given pair of parametric equations.\"},{\"question\":\"How do students complete the next set of questions?\",\"answer\":\"Rewrite each pair of parametric equations in rectangular form.\"},{\"question\":\"What is required for the critical thinking questions?\",\"answer\":\"Write two parametric representations of the same function, then modify the speed (slower/faster) and, for one question, use an opposite orientation.\"}]","Infinite Precalculus Parametric Equations - Worksheet 05 - Parametric Equations | PDF",1791426969]