[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523540-105":59,"doc-detail-523540-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","infinite-precalculus-polar-coordinates-worksheet","Infinite Precalculus - Polar Coordinates - Worksheet","","Practice worksheet focused on working with polar coordinates in Infinite Precalculus. Students plot points from given polar coordinates, find equivalent polar coordinate pairs for the same point, and convert between polar and rectangular forms. Tasks also include determining the distance between two points described in polar coordinates. A critical-thinking scenario models radar-detected plane positions using polar coordinates and asks for estimated speed over a time interval. ",{"@graph":69,"@context":122},[70,84,105],{"@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-polar-coordinates-worksheet/523540/",{"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-polar-coordinates-worksheet/523540.png","ImageObject",300,407,{"name":92,"@type":93},"hdkawk","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What kinds of problems are included in this polar coordinates worksheet?","Question",{"text":112,"@type":113},"It covers plotting points from polar coordinates, finding equivalent polar coordinate pairs for the same point, converting between polar and rectangular coordinates, and calculating distance between two polar-described points.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you find all pairs of polar coordinates that describe the same point?",{"text":117,"@type":113},"Use the worksheet’s idea of equivalence in polar form, where different angles (e.g., adding full rotations) and related radius representations can correspond to the same location.",{"name":119,"@type":110,"acceptedAnswer":120},"How is the plane’s speed estimated in the critical-thinking question?",{"text":121,"@type":113},"Two radar readings provide polar coordinates at two time points; the worksheet then uses the straight-line distance traveled and the elapsed 30 seconds to estimate miles per hour.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},523540,1791481852,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},3985747859855,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Kuta Software-Infinite Precalculus Polar Coordinates  \nPlot the point with the given polar coordinates.  \n1) (􀀖 , 􀀔􀀘􀀓°)  \n􀀜􀀓°  \n􀀔􀀕􀀓°  \n􀀔􀀘􀀓°  \n􀀔􀀛􀀓°  \n􀀕􀀔􀀓°  \n􀀕􀀗􀀓°  \n􀀓°  \n􀀕􀀚􀀓°  \n3) (􀀖 , ~~ ~~􀀔~~ ~~􀀔􀀙􀁓~~ ~~)    \n􀁓  \n􀀖 􀀖􀁓 􀀖  \n􀀕  \nName  Date  Period   \n2) (􀀕 , 􀀐􀀕􀀘􀀘°)  \n􀀜􀀓°  \n􀀔􀀕􀀓°  \n􀀔􀀘􀀓°  \n􀀔􀀛􀀓°  \n􀀕􀀔􀀓°  \n􀀕􀀗􀀓°  \n􀀓°  \n􀀕􀀚􀀓°  \n4) (􀀐􀀖 , 􀀕􀀖􀀔~~ ~~)  \n􀁓  \n􀀖 􀀖􀁓 􀀖  \n􀀕  \nFind all pairs of polar coordinates that describe the same point as the provided polar coordinates.  \n5) (􀀗 , 􀀜􀀓°) 6) (􀀕 , ~~ ~~􀀔􀀔􀀔~~ ~~)  \nConvert each pair of polar coordinates to rectangular coordinates.  \n7) (􀀕 , ~~ ~~􀀖􀁓􀀕~~ ~~) 8) ( 􀀔 , ~~ ~~􀀘~~ ~~)  \nConvert each pair of rectangular coordinates to polar coordinates where r 􀀡 􀀓 and 􀀓 􀁤 􀁔 􀀟 􀀕􀁓 .  \n9) (~~ ~~􀀖~~ ~~􀀕~~ ~~􀀖~~ ~~, 􀀖􀀕~~ ~~) 10) ( 􀀐 􀀕 , 􀀕 )  \nTwo points are specified using polar coordinates. Find the distance between the points.  \n11) (􀀕 , ~~ ~~~~ ~~),(􀀕 , ~~ ~~􀀔~~ ~~􀀔􀀙􀁓~~ ~~) 12) (􀀗 , ~~ ~~􀀚􀀔~~ ~~),(􀀕 , ~~ ~~~~ ~~)  \nCritical thinking question:  \n13) An air traffic controller's radar display uses polar coordinates. A passing plane is detected at 􀀕􀀛􀀘° counter-clockwise from north at a distance of 􀀖 miles from the radar. Thirty seconds later the plane is detected at 􀀕􀀕􀀘° and 􀀕 miles. Estimate the plane's speed in miles per hour.  \nKuta Software-Infinite Precalculus Polar Coordinates  \nPlot the point with the given polar coordinates.  \n1) (􀀖 , 􀀔􀀘􀀓°)  \n􀀜􀀓°  \n􀀔􀀕􀀓°  \n􀀔􀀘􀀓°  \n􀀔􀀛􀀓°  \n􀀕􀀔􀀓°  \n􀀕􀀗􀀓°  \n􀀓°  \n􀀕􀀚􀀓°  \n3) (􀀖 , ~~ ~~􀀔~~ ~~􀀔􀀙􀁓~~ ~~)    \n􀁓  \n􀀖 􀀖􀁓 􀀖  \n􀀕  \nName  Date  Period   \n2) (􀀕 , 􀀐􀀕􀀘􀀘°)  \n􀀜􀀓°  \n􀀔􀀕􀀓°  \n􀀔􀀘􀀓°  \n􀀔􀀛􀀓°  \n􀀕􀀔􀀓°  \n􀀕􀀗􀀓°  \n􀀓°  \n􀀕􀀚􀀓°  \n4) (􀀐􀀖 , 􀀕􀀖􀀔~~ ~~)  \n􀁓  \n􀀖 􀀖􀁓 􀀖  \n􀀕  \nFind all pairs of polar coordinates that describe the same point as the provided polar coordinates.  \n5) (􀀗 , 􀀜􀀓°)  \n(􀀗 , 􀀜􀀓° + 360n°) and (􀀐􀀗 , 􀀕􀀚􀀓° + 360n°) where n is an integer  \n6) (􀀕 , ~~ ~~􀀔􀀔􀀔~~ ~~)  \n(􀀕 , ~~ ~~􀀔􀀔􀀔~~ ~~ 􀀎 􀀕n􀁓 ) and (􀀐􀀕 , ~~ ~~􀀔􀀔􀀔~~ ~~ 􀀎 (􀀕n 􀀎 􀀔)􀁓 )  \nwhere n is an integer  \nConvert each pair of polar coordinates to rectangular coordinates.  \n7) (􀀕 , ~~ ~~􀀖􀁓􀀕~~ ~~)  \n(􀀓 , 􀀐􀀕)  \n8) ( 􀀔 , ~~ ~~􀀘~~ ~~)  \n( 􀀐~~ ~~􀀕􀀖~~ ~~, 􀀔􀀕~~ ~~)  \nConvert each pair of rectangular coordinates to polar coordinates where r 􀀡 􀀓 and 􀀓 􀁤 􀁔 􀀟 􀀕􀁓 .  \n9) (~~ ~~􀀖~~ ~~􀀕~~ ~~􀀖~~ ~~, 􀀖􀀕~~ ~~)  \n(􀀖 , ~~ ~~~~ ~~)  \n10) ( ,  􀀕􀀖􀁓􀀗, ) 􀀕 )  \nTwo points are specified using polar coordinates. Find the distance between the points.  \n11) (􀀕 , ~~ ~~~~ ~~),(􀀕 , ~~ ~~􀀔~~ ~~􀀔􀀙􀁓~~ ~~)  \n􀀕 􀀕 􀁼 􀀕􀀑􀀛􀀕􀀛  \n12) (􀀗 , ~~ ~~􀀚􀀔~~ ~~),(􀀕 , ~~ ~~~~ ~~)  \n􀀕 􀀘 􀁼 􀀗􀀑􀀗􀀚􀀕  \nCritical thinking question:  \n13) An air traffic controller's radar display uses polar coordinates. A passing plane is detected at 􀀕􀀛􀀘° counter-clockwise from north at a distance of 􀀖 miles from the radar. Thirty seconds later the plane is detected at 􀀕􀀕􀀘° and 􀀕 miles. Estimate the plane's speed in miles per hour.  \nAssuming a straight path, no acceleration, no change in altitude, and no curviture of the earth. 􀀔􀀕􀀓 􀀚 􀁼 􀀖􀀔􀀚􀀑􀀗􀀜mph  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCainmRMXqyrxdR","https://ap.wps.com/l/cbCainmRMXqyrxdR","pdf",39711,"English","# Plot Points with Polar Coordinates\n# Find Equivalent Polar Coordinates\n# Convert Polar to Rectangular and Back\n# Determine Distance Between Two Polar Points\n# Critical Thinking: Radar Plane Speed","[{\"question\":\"What kinds of problems are included in this polar coordinates worksheet?\",\"answer\":\"It covers plotting points from polar coordinates, finding equivalent polar coordinate pairs for the same point, converting between polar and rectangular coordinates, and calculating distance between two polar-described points.\"},{\"question\":\"How do you find all pairs of polar coordinates that describe the same point?\",\"answer\":\"Use the worksheet’s idea of equivalence in polar form, where different angles (e.g., adding full rotations) and related radius representations can correspond to the same location.\"},{\"question\":\"How is the plane’s speed estimated in the critical-thinking question?\",\"answer\":\"Two radar readings provide polar coordinates at two time points; the worksheet then uses the straight-line distance traveled and the elapsed 30 seconds to estimate miles per hour.\"}]","Infinite Precalculus - Polar Coordinates - Worksheet | PDF",1791426978]