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

2. 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.

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

4. 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)

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

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

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

8. Half Angle Formulas

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

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

11. Example 7
Given , find the value of .