[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523518-105":59,"doc-detail-523518-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","equations-and-multiple-angle-identities-worksheet-practice","Equations and Multiple-Angle Identities - Worksheet Practice","","Equations and Multiple-Angle Identities worksheet for Infinite Precalculus practice. Students solve 16 trigonometric equations, first finding solutions for each equation and then determining all solutions in degrees. Problems include equations with sine and cosine and multiple-angle expressions, plus a critical thinking prompt requiring an equation involving cos x and sin with no solution. A final hint encourages creating similar worksheets using Infinite Precalculus.",{"@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/equations-and-multiple-angle-identities-worksheet-practice/523518/",{"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/equations-and-multiple-angle-identities-worksheet-practice/523518.png","ImageObject",300,407,{"name":92,"@type":93},"dhado","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main task of this worksheet?","Question",{"text":112,"@type":113},"Solve each given trigonometric equation and then find all solutions in degrees for the listed problems.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which trigonometric functions appear in the equations?",{"text":117,"@type":113},"The worksheet uses sine (sin) and cosine (cos) and combines them with multiple-angle expressions.",{"name":119,"@type":110,"acceptedAnswer":120},"What does problem 17 ask students to do?",{"text":121,"@type":113},"Write an equation involving cos x and sin that has no solution.","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},523518,1791732544,{"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":34,"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},5909893218464,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Kuta Software-Infinite Precalculus Name   \nEquations and Multiple-Angle Identities Date  Period   \nSolve each equation for 􀀓 􀁤 􀁔 􀀟 􀀕􀁓 .  \n1) 􀀐sin 􀀕􀁔 􀀠 􀀕 sin 􀁔 􀀐 􀀕sin 􀀕􀁔 2) 􀀐􀀕 cos 􀁔 􀀠 sin 􀀕􀁔 􀀐 cos 􀁔  \n3) 􀀓 􀀠 cos 􀀕􀁔 􀀎 􀀖sin 􀁔 􀀎 􀀗sin􀀕 􀁔 4) cos 􀁔 􀀎 cos 􀀕􀁔 􀀠 􀀓  \n5) cos ~~ ~~􀁔􀀕 􀀠 cos 􀁔 􀀎 􀀔 6) cos 􀁔 􀀠 􀀕 􀀎 􀀖sin ~~ ~~􀁔􀀕  \n7) 􀀖 􀀎 􀀕 cos 􀁔 􀀠 􀀗 cos ~~ ~~􀁔􀀕~~ ~~ 8) 􀀖 sin ~~ ~~􀁔􀀕 􀀎 cos 􀁔 􀀠 􀀔  \nFind all solutions to each equation in degrees.  \n9) sin 􀀗x 􀀎 sin 􀀙x 􀀠 􀀓 10) 􀀓 􀀠 cos 􀀕x 􀀎 cos 􀀙x  \n11) 􀀓 􀀠 cos 􀀛 x 􀀎 cos 􀀙x 12) cos x 􀀎 cos 􀀚x 􀀠 􀀓  \n13) sin 􀀛 x 􀀎 sin 􀀕x 􀀠 cos 􀀖 x 14) sin 􀀖 x 􀀎 sin 􀀕x 􀀎 sin 􀀗x 􀀠 􀀓  \n15) sin 􀀕x 􀀠 􀀐cos 􀀖 x 􀀎 sin 􀀗x 16) 􀀓 􀀠 sin x 􀀎 sin 􀀖 x 􀀎 sin 􀀘x  \nCritical thinking question:  \n17) Write an equation involving cos x and sin  that has no solution.  \nKuta Software-Infinite Precalculus Name   \nEquations and Multiple-Angle Identities Date  Period   \nSolve each equation for 􀀓 􀁤 􀁔 􀀟 􀀕􀁓 .  \n1) 􀀐sin 􀀕􀁔 􀀠 􀀕 sin 􀁔 􀀐 􀀕sin 􀀕􀁔 2) 􀀐􀀕 cos 􀁔 􀀠 sin 􀀕􀁔 􀀐 cos 􀁔  \n􀁞 􀀓 , ~~ ~~, 􀁓 , ~~ ~~􀀚􀁓􀀗~~ ~~􀁠 􀁞 ~~ ~~~~ ~~, ~~ ~~􀀚􀁓􀀙~~ ~~, ~~ ~~􀀖~~ ~~, ~~ ~~􀀔~~ ~~􀀔􀀙􀁓~~ ~~􀁠  \n3) 􀀓 􀀠 cos 􀀕􀁔 􀀎 􀀖sin 􀁔 􀀎 􀀗sin􀀕 􀁔 4) cos 􀁔 􀀎 cos 􀀕􀁔 􀀠 􀀓  \n􀁞 ~~ ~~􀀚􀁓􀀙~~ ~~, ~~ ~~􀀖~~ ~~, ~~ ~~􀀔~~ ~~􀀔􀀙􀁓~~ ~~􀁠 􀁞 ~~ ~~~~ ~~, 􀁓 , ~~ ~~􀀘~~ ~~􀁠  \n5) cos ~~ ~~􀁔􀀕 􀀠 cos 􀁔 􀀎 􀀔 6) cos 􀁔 􀀠 􀀕 􀀎 􀀖sin ~~ ~~􀁔􀀕  \n􀁞 ~~ ~~  \n􀀕􀁓􀀖 , 􀁓 􀁠 No solution.  \n7) 􀀖 􀀎 􀀕 cos 􀁔 􀀠 􀀗 cos  \n􀁞 ~~ ~~􀀕􀁓􀀖~~ ~~􀁠  \n 􀁔  \n􀀕  \n8)  \n􀀖 sin ~~ ~~􀁔􀀕 􀀎 cos  \n􀁞 􀀓 , 􀀕􀁓􀀖~~ ~~, 􀀗􀁓􀀖~~ ~~􀁠  \n􀁔 􀀠 􀀔  \nFind all solutions to each equation in degrees.  \n9) sin 􀀗x 􀀎 sin 􀀙x 􀀠 􀀓 10) 􀀓 􀀠 cos 􀀕x 􀀎 cos 􀀙x  \n􀁞􀀖􀀙n, 􀀜􀀓 􀀎 􀀔􀀛􀀓n􀁠 􀁞 ~~ ~~􀀗􀀘􀀕 􀀎 􀀗􀀘 n, 􀀗􀀘 􀀎 􀀜􀀓n 􀁠  \n11) 􀀓 􀀠 cos 􀀛 x 􀀎 cos 􀀙x 12) cos x 􀀎 cos 􀀚x 􀀠 􀀓  \n􀁞 ~~ ~~􀀜􀀓􀀚 􀀎 ~~ ~~􀀔~~ ~~􀀛􀀓􀀚n~~ ~~ 􀁠 􀁞 ~~ ~~􀀗􀀘􀀕 􀀎 􀀗􀀘 n, 􀀖􀀓 􀀎 􀀙􀀓n 􀁠  \n13) sin 􀀛 x 􀀎 sin 􀀕x 􀀠 cos 􀀖 x 14) sin 􀀖 x 􀀎 sin 􀀕x 􀀎 sin 􀀗x 􀀠 􀀓  \n􀁞􀀖􀀓 􀀎 􀀙􀀓n, 􀀙 􀀎 􀀚􀀕n, 􀀖􀀓 􀀎 􀀚􀀕n􀁠 􀁞􀀙􀀓n􀁠  \n15) sin 􀀕x 􀀠 􀀐cos 􀀖 x 􀀎 sin 􀀗x 16) 􀀓 􀀠 sin x 􀀎 sin 􀀖 x 􀀎 sin 􀀘x  \n􀁞􀀖􀀓 􀀎 􀀙􀀓n􀁠 􀁞􀀙􀀓n􀁠  \nCritical thinking question:  \n17) Write an equation involving cos x and sin  that has no solution.  \nMany. Ex: cos x 􀀎 sin  􀀠 􀀔􀀓􀀓  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaio7ME8ngi5Hv","https://ap.wps.com/l/cbCaio7ME8ngi5Hv","pdf",26008,"English","# Solve Trigonometric Equations\n## Solve each equation and find all solutions in degrees\n# Critical Thinking\n## Create an equation involving cos x and sin with no solution","[{\"question\":\"What is the main task of this worksheet?\",\"answer\":\"Solve each given trigonometric equation and then find all solutions in degrees for the listed problems.\"},{\"question\":\"Which trigonometric functions appear in the equations?\",\"answer\":\"The worksheet uses sine (sin) and cosine (cos) and combines them with multiple-angle expressions.\"},{\"question\":\"What does problem 17 ask students to do?\",\"answer\":\"Write an equation involving cos x and sin that has no solution.\"}]","Equations and Multiple-Angle Identities - Worksheet Practice | PDF",1791426946]