PP Section 8.2

# PP Section 8.2 - The Double-Angle Formulas For sine θ θ...

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Unformatted text preview: The Double-Angle Formulas For sine: θ θ θ cos sin 2 2 sin = θ θ θ θ θ θ θ θ θ cos sin 2 sin cos cos sin ) sin( 2 sin = + = + = For cosine: θ θ θ 2 2 sin cos 2 cos- = θ θ θ θ θ θ θ θ θ 2 2 sin cos sin sin cos cos ) cos( 2 cos- =- = + = Variations for Cosine θ θ θ 2 2 sin cos 2 cos- = θ θ θ 2 2 2 sin 2 1 sin sin 1- =-- = θ θ 2 sin 2 1 2 cos- = θ θ θ 2 2 sin cos 2 cos- = 1 cos 2 ) cos 1 ( cos 2 2 2- =-- = θ θ θ 1 cos 2 2 cos 2- = θ θ All Formulas Together 1 cos 2 2 cos sin 2 1 2 cos sin cos 2 cos 2 2 2 2- =- =- = θ θ θ θ θ θ θ θ θ θ cos sin 2 2 sin = 13 5 a b r 2 2 2 + = 5 13 2 2 2 + = b b 2 169 25 144 =- = 12 = b 12 13 12 cos- =- = r b θ θ If find the exact value of (a) sin 2 (b) cos 2 sin , , θ π θ π θ θ = < < 5 13 2 sin cos θ θ = = - 5 13 12 13 sin sin cos 2 2 θ θ θ = - = 13 12 13 5 2 = - 120 169 cos cos sin 2 2 2 θ θ θ =- 2 2 13 5 13 12 - - = =- 144 169 25 169 = 119 169 Double Angle Formula for Tangent...
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PP Section 8.2 - The Double-Angle Formulas For sine θ θ...

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