1. 7.2.2 – Sum and Difference Identities, Cont’d

2. Yesterday, we were able to cover the basics of the sum and difference identities for the basic trig functions
Rewrite angles in terms of angles we know
Express unknown angles in a new way
Exact values

3. Now, using the same identities, we may do the following:
1) Find values where θ is not necessarily known
2) Rewrite expressions in terms of a single trig function

4. No Angles Without angles, we still use the same formulas
Example. Find sin(a – b) if sin(a) = -15/17 and cos(b) = -3/5. a and b are in quadrant 3.
Already have the critical information

5. Exampke. Find the cos(a + b) if cos(a) = -24/25 and sin(b) = 5/13
Exampke. Find the cos(a + b) if cos(a) = -24/25 and sin(b) = 5/13. a and b are in quadrant 1.

6. Rewriting identities
Although only seldom seen, we can also rewrite expressions going backwards, using the sum and difference identities
1) Determine which identity is being used
2) Determine the sum or difference of the angle
3) Determine the single trig function

7. Example. Rewrite the following expression as a trig function of a single number.
sin 800 cos cos 800 sin 200

8. Example. Rewrite the following expression as a trig function of a single number.
sin 1250 cos 350 – cos sin 350

9. Example. Rewrite the following expression as a trig function of a single number.
sin cos - sin cos

10. Assignment
Pg. 564
41-57 odd
Quiz; Wednesday; Test review on Thursday