[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-572174-105":53,"doc-detail-572174-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","the-unit-circle-reference-sheet-mathematical-guide","The Unit Circle Reference Sheet - Mathematical Guide","","This comprehensive reference sheet provides an essential guide to the unit circle and its associated trigonometric ratios. It includes detailed coordinate mappings for common angles in both degrees and radians, along with fundamental trigonometric identities and definitions for unit and general circles. The document serves as an efficient study aid for trigonometry students, outlining the relationships between sine, cosine, tangent, cosecant, secant, and cotangent, while also clarifying the calculation of reference angles across different quadrants. Its structured layout enables quick access to key geometric constants and coordinate pairs, facilitating easier mastery of circular functions and their practical applications in mathematics.",{"@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/the-unit-circle-reference-sheet-mathematical-guide/572174/",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/the-unit-circle-reference-sheet-mathematical-guide/572174.png","ImageObject",442,249,{"name":88,"@type":89},"Riley","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-22","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":47},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What are the primary trigonometric ratios for the unit circle?","Question",{"text":108,"@type":109},"In the unit circle, sin(θ) = y, cos(θ) = x, and tan(θ) = y/x, while the reciprocal functions are defined as csc(θ) = 1/y, sec(θ) = 1/x, and cot(θ) = x/y.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How is the reference angle α defined?",{"text":113,"@type":109},"The reference angle α is the acute angle formed between the terminal side of an angle θ and the x-axis.",{"name":115,"@type":106,"acceptedAnswer":116},"What is the difference between unit circle and general circle equations?",{"text":117,"@type":109},"The unit circle is defined by the equation x² + y² = 1, whereas a general circle with radius r is defined by the equation x² + y² = r².","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},572174,1792122456,{"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":47,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":9,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":4},1374391975076,"https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051","The Unit Circle Reference Sheet  \n| \u003Cbr>90° | π 2 |  | \u003Cbr>60° ~~ ~~π3\u003Cbr>\u003Cbr>45° ~~ ~~π4\u003Cbr>\u003Cbr>30° ~~ ~~π6 | |  |\n| --- | --- | --- | --- | --- | --- |\n| \u003Cbr>120° ~~ ~~2π3\u003Cbr>\u003Cbr>135° ~~ ~~3π4\u003Cbr>\u003Cbr>150° ~~ ~~5π6\u003Cbr>180° π (odd ) |  |  |  |  |  |\n|  | 0° 360° 0 2π (even) |  |  |  |  |\n| \u003Cbr>210° ~~ ~~7π6\u003Cbr>\u003Cbr>225° ~~ ~~5π4\u003Cbr>\u003Cbr>240° ~~ ~~4π3 | , , |  |  |  |  |\n|  | ° | 3π\u003Cbr>2 | \u003Cbr>330° ~~ ~~116π\u003Cbr>\u003Cbr>315° ~~ ~~7π4\u003Cbr>\u003Cbr>300° ~~ ~~5π3\u003Cbr>|  | |\n| \u003Cbr>270 |  |  |  |  |  |\n\n􀂧 1 􀂨 −  􀂨 ,􀂩 2  \n􀂧  2   2  􀂷􀂨   􀂸  \n􀂨 − , 􀂸  \n􀂩 2 2 􀂹  \n􀂧  3 1 􀂷  \n􀂨 −   􀂸  \n􀂩􀂨 2 , 2 􀂹􀂸  \n3  \n2  \n(0, 1)  \n􀂷􀂸􀂸􀂹  \n􀂧 1  3 􀂷􀂨   􀂸  \n􀂨 , 􀂸  \n􀂩 2 2 􀂹  \n􀂧   2    2  􀂷􀂨   􀂸  \n􀂨 , 􀂸  \n􀂩 2 2 􀂹  \n􀂧  3 1 􀂷􀂨   􀂸  \n􀂨 , 􀂸  \n􀂩 2 2 􀂹  \n(−1, 0) (1, 0)  \n􀂧  3 1 􀂷  \n􀂨 −  −   􀂸  \n􀂨 , 􀂸  \n􀂩 2 2 􀂹  \n􀂧  2   2  􀂷  \n􀂨 −  −   􀂸  \n􀂩􀂨 2 , 2 􀂹􀂸  \n􀂧 1   3 􀂷  \n􀂨 −  −   􀂸  \n􀂨 , 􀂸  \n􀂩 2 2 􀂹  \n(0, −1)  \n􀂧  3 1 􀂷  \n􀂨   −   􀂸  \n􀂨 , 􀂸  \n􀂩 2 2 􀂹  \n􀂧􀂨   2 −   2 􀂷􀂸􀂩􀂨 2 , 2 􀂹􀂸  \n􀂧 1   3 􀂷  \n􀂨   −   􀂸  \n􀂩􀂨 2 , 2 􀂹􀂸  \n| The Unit Circle Ratios\u003Cbr>x 2 + y2 = 1 |  |  | General Circle Ratios\u003Cbr>2 2 2\u003Cbr>x + y = r |  |  |  | The Reference Angle, α , is the acute angle formed between the terminal side and the x-axis. |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| sinθ = y\u003Cbr>cos θ = x\u003Cbr>tan θ = yx | csc θ =\u003Cbr>sec θ = |  1\u003Cbr>y\u003Cbr> 1\u003Cbr>x | sinθ = yr |  | csc θ =\u003Cbr>sec θ = | r\u003Cbr>y\u003Cbr>r\u003Cbr>x |  |\n|  |  |  |  |  |  |  | \u003Cbr>θ = π − αθ = 180° − α\u003Cbr>θ = α\u003Cbr>\u003Cbr>θ = π + αθ = 180° + α\u003Cbr>θ = 2π − αθ = 360° − α |\n|  |  |  | cos θ =\u003Cbr>tan θ = | x\u003Cbr>r\u003Cbr>y\u003Cbr>x |  |  |  |\n|  | cot θ = xy |  |  |  | cot θ = xy |  |  |","cbCaisiDsAcSo8C3","https://ap.wps.com/l/cbCaisiDsAcSo8C3","pdf",189870,"English","# Unit Circle Coordinate Mappings\n## Angles and Radians\n## Coordinate Points\n# Trigonometric Ratios and Definitions\n## Unit Circle Ratios\n## General Circle Ratios\n## Reference Angles","[{\"question\":\"What are the primary trigonometric ratios for the unit circle?\",\"answer\":\"In the unit circle, sin(θ) = y, cos(θ) = x, and tan(θ) = y/x, while the reciprocal functions are defined as csc(θ) = 1/y, sec(θ) = 1/x, and cot(θ) = x/y.\"},{\"question\":\"How is the reference angle α defined?\",\"answer\":\"The reference angle α is the acute angle formed between the terminal side of an angle θ and the x-axis.\"},{\"question\":\"What is the difference between unit circle and general circle equations?\",\"answer\":\"The unit circle is defined by the equation x² + y² = 1, whereas a general circle with radius r is defined by the equation x² + y² = r².\"}]","The Unit Circle Reference Sheet - Mathematical Guide | PDF",1791925925]