1. Identities: Cofunction, Double-Angle and Half-Angle
Section 7.2
Identities: Cofunction, Double-Angle and Half-Angle
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2. Objectives Use cofunction identities to derive other identities.
Use the double-angle identities to find function values of twice an angle when one function value is known for that angle.
Use the half-angle identities to find function values of half an angle when one function value is known for that angle.
Simplify trigonometric expressions using the double-angle identities and the half-angle identities.

3. Cofunction Identities

4. Example
Prove the identity
Solution:

5. Cofunction Identities

6. Example
Find an identity for each of the following.
Solution:

7. Double-Angle Identities

8. Other Useful Identities

9. Example Find an equivalent expression for each of the following.
Solution:

10. Example (cont)

11. Half-Angle Identities

12. Example
Find tan (π/8) exactly. Then check the answer using a graphing calculator in RADIAN mode.
Solution:

13. Example
Simplify each of the following.
Solution: