7.2.2 – Sum and Difference Identities, Cont’d

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. 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 800cos 200 - cos 800 sin 200

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