7.2.2 – Sum and Difference Identities, Cont’d

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

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

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

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.

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

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

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

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

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