1. 14. DOUBLE-ANGLE and HALF ANGLE IDENTITIES

2. Double Angle Formulas Half Angle Formulas The + or – depends in
which quadrant the original
given value exists

3. Two types of double angle problems
1. verify/simplify 2. given a trig value find values of double angles

4. Type 1

5. Simplify

6. Simplify

7. Simplify

8. Simplify

9. Verify the identity

10. Verify the identity

11. Prove

12. Type 2

13. Let's draw a picture. 5 4   -3

14. Let's draw a picture.  1  4

15. Half Angle

17. Ex: Use the half angle formula to find the exact value of sin(105o)
105 exists in the II, so sine is positive!
2. Double 105 to get
the numerator
3. Plug into the half formula 4.
5. Simplify

23. Find the exact value of the function.