10.3 Double Angle and Half Angle Formulas

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Presentation transcript:

10.3 Double Angle and Half Angle Formulas

Double Angle for Sine

Double Angle for Cosine

Double Angle for Tangent

If Find:

Find a formula for sin4x

Half Angle Formula for Sine Start with a double angle formula Notice that the contents of the parentheses on the left is twice that of the parentheses on the right. Rewrite the equation, keeping this fact true.

Half Angle Formula for Cosine Start with another double angle formula Notice that the contents of the parentheses on the left is twice that of the parentheses on the right. Rewrite the equation, keeping this fact true.

Find the exact value of cos (5/8) Why is this negative?

Find the exact value of sin (/12)

Half Angle Formula for Tangent

Half Angle Formula for Tangent If you rationalize the denominator: Multiply by the conjugate

Half Angle Formula for Tangent If you rationalize the numerator: Multiply by the conjugate

Simplify the expression:

Find the values of sin(2x), cos(2x) & tan(2x) using the given information Angle x is obtuse and

Find the values of sin(2x), cos(2x) & tan(2x) using the given information Angle x is acute and