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Post1330_section6o2 - 2 b When calculating trigonometric...

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Section 6.2 – Double-Angle and Half-Angle Formulas 1 Section 6.2 Double-Angle and Half-Angle Formulas The following, most useful, basic identities follow from the addition formulas. Note: In the half-angle formulas the ± symbol is intended to mean either positive or negative but not both, and the sign before the radical is determined by the quadrant in which the angle 2 θ terminates. Example 1: Suppose 4 sin 5 θ = - and 3 2 π π θ < < . a. Find ( sin 2 θ . b. Find cos 2 θ . Double-Angle Formulas 2 2 2 sin(2 ) 2sin cos cos(2 ) cos sin 2tan tan(2 ) 1 tan θ θ θ θ θ θ θ θ θ = = - = - Half-Angle Formulas 1 cos sin 2 2 1 cos cos 2 2 sin tan 2 1 cos θ θ θ θ θ θ θ - = ± + = ± =
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Unformatted text preview: 2 b When calculating trigonometric functions of multiples of 12 π , you have the choice of using an addition formula or using a half-angle formula. b When calculating trigonometric functions of multiples of 8 , you have only one choice: a half-angle formula. It is not possible to write 8 as a sum or difference of our special angles 3 , 6 , and 4 !!! Example 2: Calculate cos 8 . Example 3: Use the half-angle formula to calculate 12 13 sin ....
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