[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571379-105":53,"doc-detail-571379-en":127},{"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":120,"head_meta":122,"extra_data":124,"updated_unix":126},105,"en","trig-cheat-sheet-quick-reference","Trig Cheat Sheet - Quick Reference","","Comprehensive trig cheat sheet compiling definitions, domains, ranges, key facts, and core function relationships for sine, cosine, tangent, cosecant, secant, and cotangent. Includes period rules, reciprocal and Pythagorean identities, even/odd and periodic properties, and a broad set of angle formulas: double-angle, half-angle, sum and difference, product-to-sum, sum-to-product, and cofunction forms. Also covers unit circle mappings, inverse trig definitions with domains/ranges and inverse properties, and commonly used triangle laws such as the Law of Sines, Law of Cosines, and Mollweide’s formula.",{"@graph":63,"@context":119},[64,80,102],{"@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/trig-cheat-sheet-quick-reference/571379/",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/trig-cheat-sheet-quick-reference/571379.png","ImageObject",442,249,{"name":88,"@type":89},"Malam Tenang","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-24","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",7,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"What is the domain and range for common trigonometric functions on the cheat sheet?","Question",{"text":109,"@type":110},"The sheet states the domain as the values of θ that can be substituted into each function, and lists valid output ranges for sin, cos, and cosecant/ secant/tangent/cotangent. It also specifies angle restrictions for tan, csc, sec, and cot.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"What core identities are provided for trigonometric functions?",{"text":114,"@type":110},"It includes reciprocal identities (e.g., csc, sec, cot in terms of sin, cos, tan), Pythagorean identities relating sin/cos and tan/cot to sec and csc, and tangent/cotangent identities.",{"name":116,"@type":107,"acceptedAnswer":117},"Which angle formulas and triangle laws are included?",{"text":118,"@type":110},"The document provides double-angle, half-angle, sum and difference, product-to-sum, sum-to-product, and cofunction formulas. It also lists the Law of Sines, Law of Cosines, and Mollweide’s formula for triangles.","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},571379,1792009239,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":79,"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":73},962093532863,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Trig Cheat Sheet  \nDefinition of the Trig Functions  \nRight triangle definition  \nFor this definition we assume that 0 \u003C θ \u003C ~~ ~~π2 or 0°\u003C θ \u003C 90° .  \nsinθ = ~~ h~~oppoypoteteuse cos θ =  adjacent  hypotenuse  \ntan θ =  opposite adjacent  \ncsc θ = ~~ ~~hypotenusoppos~~i~~tee sec θ =  hypotenuse adjacent  \ncot θ =  adjacent opposite  \nFacts and Properties  \nDomain  \nThe domain is all the values of θ that can be plugged into the function.  \nsinθ , θ can be any angle cos θ , θ can be any angle  \ntan θ , θ ≠ ⎛⎜⎝ n + ~~ ~~12⎟ π , n = 0, ±1, ± 2,… csc θ , θ ≠ n π , n = 0, ±1, ± 2,… sec θ , θ ≠ ⎛⎜⎝ n + ~~ ~~12⎟ π , n = 0, ±1, ± 2,… cot θ , θ ≠ n π , n = 0, ±1, ± 2,…  \nRange  \nThe range is all possible values to get out of the function.  \n−1≤ sinθ ≤ 1 csc θ ≥ 1 and cscθ ≤ −1 −1 ≤ cosθ ≤ 1 sec θ ≥ 1 and secθ ≤ −1 −∞ ≤ tan θ ≤ ∞ −∞ ≤ cot θ ≤ ∞  \nPeriod  \nThe period of a function is the number, T, such that f (θ+ T) = f (θ ) . So, if ω is a fixed number and θ is any angle we have the following periods.  \nsin (ωθ ) → T = ~~ ~~2πω cos (ωθ ) → T = ~~ ~~2πω tan (ωθ ) → T = ~~ ~~πω csc (ωθ ) → T = ~~ ~~2πω sec (ωθ ) → T = ~~ ~~2πω cot (ωθ ) → T = ~~ ~~πω  \n© 2005 Paul Dawkins  \nFormulas and Identities  \nTangent and Cotangent Identities  \ntan θ = ~~ ~~scθ~~θ ~~ cot θ = ~~ ~~coss~~i~~nθ~~θ~~  \nReciprocal Identities  \ncsc θ = ~~ si~~1n~~ θ ~~ sinθ = ~~ ~~cs1c~~ θ ~~sec θ = ~~ ~~co1s~~ ~~θ~~ ~~ cos θ = ~~ ~~se1c~~ ~~θ cot θ = ~~ ~~ta1n~~ ~~θ~~ ~~ tan θ = ~~ ~~1cot~~ ~~θ  \nPythagorean Identities  \nsin 2 θ + cos2 θ = 1  \ntan 2 θ +1 = sec2 θ 1+ cot 2 θ = csc2 θ  \nEven/Odd Formulas  \nsin (−θ ) = − sinθ cos (−θ ) = cos θ tan (−θ ) = − tan θ  \nPeriodic Formulas  \nIf n is an integer.  \ncsc (−θ ) = − csc θ sec (−θ ) = sec θ cot (−θ ) = − cot θ  \nsin (θ+ 2π n) = sinθ csc (θ+ 2π n) = csc θ cos (θ+ 2π n) = cos θ sec (θ+ 2π n) = sec θ tan (θ+ π n) = tan θ cot (θ+ π n) = cot θ  \nDouble Angle Formulas  \nsin ( 2 θ ) = 2 sinθcos θ cos ( 2 θ ) = cos2 θ − sin 2 θ  \n= 2 cos2 θ −1  \n= 1− 2 sin 2 θ tan ( 2 θ ) = 1ttanan~~θ~~  \nDegrees to Radians Formulas  \nIf x is an angle in degrees and t is an angle in radians then  \n~~ ~~π~~ ~~ =  t  ⇒ t = ~~ ~~π~~ ~~x~~ ~~ and x = 180t 180 x 180 π  \nHalf Angle Formulas  \nsin 2 θ = ~~ ~~12 ( 1− cos ( 2 θ ))  \ncos2 θ = ~~ ~~12 ( 1+ cos ( 2θ ))  \ntan 2 θ = ~~ ~~11~~ ~~coscos(~~( ~~22θ~~θ~~)~~)~~  \nSum and Difference Formulas  \nsin ( α ± β ) = sin α cos β ± cosα sin β cos ( α ± β ) = cosα cos β ∓ sin α sin β tan ( α ± β ) = 1tntαantantanβ~~β~~  \nProduct to Sum Formulas  \nsin α sin β = ~~ ~~12 cos ( α − β ) − cos( α + β ) cosα cos β = ~~ ~~12 cos ( α − β ) + cos( α + β ) sin α cos β = ~~ ~~12 sin ( α + β ) + sin ( α − β ) cosα sin β = ~~ ~~12 sin ( α + β ) − sin ( α − β )  \nSum to Product Formulas  \nsin α + sin β = 2 sin ⎝⎜⎛ ~~ ~~α~~ ~~+2~~ ~~β ⎟ cos ⎜ ~~ ~~α~~ ~~−2~~ ~~β~~ ~~ ⎟ sin α − sin β = 2 cos ⎝⎜⎛ ~~ ~~α~~ ~~+2~~ ~~β ⎟ sin ⎜ ~~ ~~α~~ ~~−2~~ ~~β~~ ~~ ⎟ cosα + cos β = 2 cos ⎝⎜⎛ ~~ ~~α~~ ~~+2~~ ~~β ⎟ cos ⎜ ~~ ~~α~~ ~~−2~~ ~~β~~ ~~ ⎟ cosα − cos β = −2sin ⎝⎜⎛ ~~ ~~α~~ ~~+2~~ ~~β ⎟ sin ⎜ ~~ ~~α~~ ~~−2~~ ~~β~~ ~~ ⎟  \nCofunction Formulas  \nsin ⎛⎜⎝ ~~ ~~π2~~ ~~ −θ⎟ = cos csc ⎛⎜⎝ ~~ ~~π2~~ ~~ −θ⎟ = sectan ⎛⎜⎝ ~~ ~~π2~~ ~~ −θ⎟ = cot  \nθ  \nθ  \nθ  \ncos ⎛⎜⎝ ~~ ~~π2~~ ~~ −θ⎟ = sin sec ⎛⎜⎝ ~~ ~~π2~~ ~~ −θ⎟ = csc  \ncot ⎛⎜⎝ ~~ ~~π2~~ ~~ −θ⎟ = tan  \nθ  \nθ  \nθ  \n© 2005 Paul Dawkins  \nUnit Circle  \n( −1,0) π 180°  \n|  |  |  |\n| --- | --- | --- |\n| ( 0 | ,1) |  |\n|  |  |  |\n| π 2 |  |  |\n|  |  |  |\n| 90° |  |  |\n\n| 0° |\n| --- |\n| 360° |\n\n\n| 0 | ( 1 0) |  |\n| --- | --- | --- |\n|  |  | , |\n| 2π | | x |\n\nFor any ordered pair on the unit circle ( x, y ) : cos θ = x and sinθ = y  \nExample  \ncos ⎜ ~~ ~~5π3~~ ~~ ⎟ = ~~ ~~12~~ ~~ sin ⎜ ~~ ~~5π3~~ ~~ ⎟ = −~~ ~~23  \n© 2005 Paul Dawkins  \nInverse Trig Functions  \nDefinition  \ny = sin −1 x is equivalent to x = sin yy = cos−1 x is equivalent to x = cosyy = tan −1 x is equivalent to x = tan y  \nDomain and Range  \nFunction Domain  \ny = sin −1 x −1≤ x ≤ 1  \ny = cos−1 x −1≤ x ≤ 1  \ny = tan −1 x −∞ \u003C x \u003C ∞  \nRange −","cbCaic4uJI3fCdu2","https://ap.wps.com/l/cbCaic4uJI3fCdu2","pdf",48620,"English","# Definition of the Trig Functions\n## Facts and Properties\n# Formulas and Identities\n## Tangent and Cotangent Identities\n## Reciprocal Identities\n## Pythagorean Identities\n## Even/Odd and Periodic Formulas\n## Double-Angle and Half-Angle Formulas\n## Sum/Difference and Product/Sum Formulas\n## Cofunction Formulas\n# Unit Circle\n# Inverse Trig Functions\n## Definition and Domain/Range\n## Inverse Properties\n# Law of Sines, Cosines and Tangents\n## Law of Sines\n## Law of Cosines\n## Mollweide’s Formula","[{\"question\":\"What is the domain and range for common trigonometric functions on the cheat sheet?\",\"answer\":\"The sheet states the domain as the values of θ that can be substituted into each function, and lists valid output ranges for sin, cos, and cosecant/ secant/tangent/cotangent. It also specifies angle restrictions for tan, csc, sec, and cot.\"},{\"question\":\"What core identities are provided for trigonometric functions?\",\"answer\":\"It includes reciprocal identities (e.g., csc, sec, cot in terms of sin, cos, tan), Pythagorean identities relating sin/cos and tan/cot to sec and csc, and tangent/cotangent identities.\"},{\"question\":\"Which angle formulas and triangle laws are included?\",\"answer\":\"The document provides double-angle, half-angle, sum and difference, product-to-sum, sum-to-product, and cofunction formulas. It also lists the Law of Sines, Law of Cosines, and Mollweide’s formula for triangles.\"}]","Trig Cheat Sheet - Quick Reference | PDF",1791914548]