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Section 74.notebook December 16, 2016 Sec. 7.4 Double Angle & HalfAngle Identites Find an expression for sin 2θ Find an expression for cos 2θ Mar 178:41 AM Double Angle Identities: 1. sin 2θ = 2sinθcosθ 2. cos 2θ = cos2θ - sin2θ (you can get other variations of this if you substitute 1 - cos2θ in for sin2θ and 1 - sin2θ in for cos2θ) Nov 128:46 AM What was your favorite cartoon when you were younger? 3. tan 2θ = 2tanθ 1 - tan2θ Jan 2011:09 AM Dec 157:50 AM Examples: Find the exact value of each function if sin θ = 3/4 and the terminal side of θ is in Quad. I a.) sin 2θ b.) cos 2θ Half Angle Identities: 1. sin α/2 = ±√((1cosα)/2) 2. cos α/2 = ±√((1+cosα)/2) c.) tan 2θ 3. tan α/2 = ±√((1 cos α)/(1 + cosα)) where cos α ≠ 1 Nov 129:03 AM Jan 2011:14 AM 1 Section 74.notebook December 16, 2016 Examples: Use a HalfAngle identity to find the exact value of tan 15o Verify that cos 2x = cot x 1 1 + sin 2x cot x + 1 Use a HalfAngle identity to find the exact value of cos π 8 Nov 133:27 PM Verify 1 cos 2xsec2x = tan2x Nov 133:33 PM Assignment: Sec. 7.4 p. 454 #16, 2127 (odds), 34, 40, 44 • I can use algebraic manipulation and established trigonometric identities to verify other trigonometric identities. Nov 133:43 PM Apr 172:46 PM 2