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3.5 double & half angle - Math 114 Section 3.5...

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Math 114 Section 3.5 Double-angle & Half-angle Formulas Section 2 A. Double-angle Formulas ( 29 ( 29 θ θ θ θ θ θ 2 2 sin cos 2 cos cos sin 2 2 sin - = = 1 cos 2 sin 2 1 2 2 - = - = θ θ ( 29 θ θ θ 2 tan 1 tan 2 2 tan - = Find the exact values of the following trigonometric functions. 1. Given , 5 3 cos = θ 2 0 π θ < < , find a) ( 29 θ 2 sin b) ( 29 θ 2 tan 2. Given , 2 1 tan = θ 2 3 π θ π < < , find ( 29 θ 2 cos . 3. Given , 5 csc - = θ 0 cos < , find ( 29 θ 2 tan .
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Use double-angle formulas to establish the following identities. 1. ( 29 θ θ θ θ θ 2 cos tan cot tan cot = + - 2. ( 29 θ θ θ csc sec 2 1 2 csc = 3. ( 29 ( 29 1 cot 1 cot 2 sin 1 2 cos + - = + θ θ θ θ B. Half-angle Formulas α α α α α α α sin cos 1 2 tan 2 cos 1 2 cos 2 cos 1 2 sin - = + ± = - ± = where the + or - sign is determined by the quadrant of the angle of 2 α α α cos 1 sin + =
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Find the exact values of the following trigonometric functions.
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