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Tasks guide students to use identities to compute exact values of expressions involving sine, cosine, tangent, cotangent, and secant at specified angles such as 120°, 60°, 45°, 165°, and selected radian measures. Several items require applying angle constraints like 270° \u003C θ \u003C 360° or π-based intervals to find unknown trigonometric values (sin 2θ, cos 2θ, tan 2θ, or related 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is the main goal of this worksheet?","Question",{"text":112,"@type":113},"To use double-angle and half-angle identities to find exact trigonometric values for given expressions and angles.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which trigonometric functions are practiced?",{"text":117,"@type":113},"Sine, cosine, tangent, cotangent, and secant appear across the problems.",{"name":119,"@type":110,"acceptedAnswer":120},"How do the angle conditions affect the problems?",{"text":121,"@type":113},"They restrict θ to a specified interval (in degrees or radians), helping determine the correct exact value when using identities like sin 2θ or tan 2θ.","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},522630,1791711020,{"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},1099514068365,"https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1794309523707217728","Kuta Software-Infinite Algebra 2 Name   \nDouble-and Half-Angle Identities Date  Period   \nUse a double-angle identity to find the exact value of each expression.  \n1) sin 120° 2) tan 60°  \n3) cos ~~ ~~4π3~~ ~~ 4) sin ~~ ~~5π3~~ ~~  \nUse a half-angle identity to find the exact value of each expression.  \n5) tan 45° 6) sin 165°  \n5π  8) cos 30°  \n7) sin  \n6  \nUse a double-angle or half-angle identity to find the exact value of each expression.  \n9) cot π3~~ ~~ 10) cot 2π3~~ ~~  \n5π 12) cot 60°  \n11) sec  12  \n13) cot 240° 5π  \n14) cot  3   \n15) sin θ = − ~~ ~~725 and 270° \u003C θ \u003C 360° Find cos ~~ ~~θ2  \n17) cos θ = ~~ ~~45 and 270° \u003C θ \u003C 360° Find sin 2θ  \n19) cos θ = − ~~ ~~45 and 90° \u003C θ \u003C 180° Find sin ~~ ~~θ2  \n21) tan θ = − ~~ ~~724 and ~~ ~~3π2~~ ~~ \u003C θ \u003C 2π Find cot ~~ ~~θ2  \n23) cot θ = ~~ ~~43 and π \u003C θ \u003C ~~ ~~3π2 Find cot 2θ  \n25) sin θ = − ~~ ~~35 and ~~ ~~3π2~~ ~~ \u003C θ \u003C 2π Find tan ~~ ~~θ2  \n16)  \n18)  \n20)  \n22)  \n24)  \n26)  \ncos θ = ~~ ~~13 and 0° \u003C θ \u003C 90° Find sin 2θ  \ncos θ = ~~ ~~2~~ ~~5~~ ~~ and 0° \u003C θ \u003C 90° Find sin ~~ ~~θ2  \ncos θ = − ~~ ~~1517 and 180° \u003C θ \u003C 270° Find tan ~~ ~~θ2  \ncot θ = ~~ ~~43 and π \u003C θ \u003C ~~ ~~3π2 Find sin 2θ  \ntan θ = 2 and 0 \u003C θ \u003C π2 Find sin ~~ ~~θ2  \ncot θ = − ~~ ~~3~~ ~~991~~ ~~ and Find sin ~~ ~~θ2  \n3π  \n2  \n\u003C θ \u003C 2π  \nKuta Software-Infinite Algebra 2 Name   \nDouble-and Half-Angle Identities Date  Period   \nUse a double-angle identity to find the exact value of each expression.  \n1) sin 120°  \n3  \n2  \n3) cos ~~ ~~4π3~~ ~~  \n 1  \n−  \n2  \n2) tan 60°  \n3  \n4) sin ~~ ~~5π3~~  ~~ 3  \n−  \n2  \nUse a half-angle identity to find the exact value of each expression.  \n5) tan 45° 1  \n7) sin ~~ ~~5π6~~ ~~  \n 1  \n2  \n6) sin 165°  \n6 − 2  \n4  \n8) cos 30°  \n3  \n2  \nUse a double-angle or half-angle identity to find the exact value of each expression.  \n9) cot π3  3  \n3  \n11) sec ~~ ~~51π2  \n6 + 2  \n13) cot 240°  \n3  \n3  \n10) cot 2π3~~  ~~ 3  \n−  \n3  \n12) cot 60°  \n3  \n3  \n14) cot ~~ ~~5π3~~  ~~ 3  \n−  \n3  \n15) sin θ = − ~~ ~~725 and 270° \u003C θ \u003C 360° Find cos ~~ ~~θ2  \n7 2  \n−  \n10  \n17) cos θ = ~~ ~~45 and 270° \u003C θ \u003C 360° Find sin 2θ  \n24  \n−  \n25  \n19) cos θ = − ~~ ~~45 and 90° \u003C θ \u003C 180° Find sin ~~ ~~θ2  \n3 10  \n10  \n21) tan θ = − ~~ ~~724 and ~~ ~~3π2~~ ~~ \u003C θ \u003C 2π Find cot ~~ ~~θ2  \n−7  \n23) cot θ = ~~ ~~43 and π \u003C θ \u003C ~~ ~~3π2 Find cot 2θ  \n 7   \n24  \n25) sin θ = − ~~ ~~35 and ~~ ~~3π2~~ ~~ \u003C θ \u003C 2π Find tan ~~ ~~θ2  \n 1  \n−  \n3  \n16) cos θ = ~~ ~~13 and 0° \u003C θ \u003C 90° Find sin 2θ  \n4 2  \n9  \n18) cos θ = ~~ ~~2~~ ~~5~~ ~~ and 0° \u003C θ \u003C 90° Find sin ~~ ~~θ2  \n10  \n20) cos θ = − ~~ ~~1517 and 180° \u003C θ \u003C 270° Find tan ~~ ~~θ2  \n−4  \n22) cot θ = ~~ ~~43 and π \u003C θ \u003C ~~ ~~3π2 Find sin 2θ  \n24  \n25  \n24) tan θ = 2 and 0 \u003C θ \u003C π2 Find sin ~~ ~~θ2  \n50 − 10 5  \n10  \n26) cot θ = − ~~ ~~3~~ ~~991~~ ~~ and ~~ ~~3π2~~ ~~ \u003C θ \u003C 2π Find sin ~~ ~~θ2  \n35  \n10  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiaYG77HFKHkg","https://ap.wps.com/l/cbCaiaYG77HFKHkg","pdf",35193,"English","# Double-Angle Identities\n# Half-Angle Identities\n# Mixed Double- and Half-Angle Problems","[{\"question\":\"What is the main goal of this worksheet?\",\"answer\":\"To use double-angle and half-angle identities to find exact trigonometric values for given expressions and angles.\"},{\"question\":\"Which trigonometric functions are practiced?\",\"answer\":\"Sine, cosine, tangent, cotangent, and secant appear across the problems.\"},{\"question\":\"How do the angle conditions affect the problems?\",\"answer\":\"They restrict θ to a specified interval (in degrees or radians), helping determine the correct exact value when using identities like sin 2θ or tan 2θ.\"}]","Double-and Half-Angle Identities - Use Double- and Half-Angle Identities | PDF",1791425998]