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10.3 Double Angle and Half Angle Formulas. Double Angle for Sine.

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Presentation on theme: "10.3 Double Angle and Half Angle Formulas. Double Angle for Sine."— Presentation transcript:

1 10.3 Double Angle and Half Angle Formulas

2 Double Angle for Sine

3 Double Angle for Cosine

4 Double Angle for Tangent

5 If Find:

6 Find a formula for sin4x

7 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.

8 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.

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

10 Find the exact value of sin (  /12)

11 Half Angle Formula for Tangent

12 If you rationalize the denominator: Multiply by the conjugate

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

14 Simplify the expression:

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

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


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