Double and Half Angle Formulas

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Presentation transcript:

Double and Half Angle Formulas Dr. Barry Shildneck Fall, 2014

Double Angle Formulas Given that you know the sum and difference formulas, derive a formula for the Sine, Cosine, and Tangent of twice an angle.

Double Angle Formulas Note: The sign of the value of the double angle is taken care of by the formula.

Example 1 sin(2θ) cos(2θ) tan(2θ) csc(2θ) cot(2θ) Use the triangle to determine the Values of each of the following. sin(2θ) cos(2θ) tan(2θ) csc(2θ) cot(2θ)

Example 2 Find the values of the sin2x, cos2x, and tan2x given

Example 3 Use identities to rewrite each expression in terms of a single trigonometric function. 1) 4sinxcosx 2) 5–10cos2x

Example 4 Derive a triple angle formula for the sine. Your final answer should be written in terms of the sin(x) only.

Half Angle Formulas

Example 5 Use the half-angle formula to find the exact value of the sin105o.

Example 6 Use the half-angle formula to find the exact value of the sin112.5o.

Example 7 Given , find the value of .