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