Section 7.3 Double-Angle, Half-Angle and Product-Sum Formulas Objectives: To understand and apply the double- angle formula. To understand and apply the half-angle formula. To understand and apply product-sum formula.

Class Work 1.Evaluate csc780  2.Find the exact value of tan165 

Double-Angle Formulas Formula for sine: Formula for cosine: Formula for tangent:

Ex 1. If and x is in quadrant II, find cos 2x, sin 2x, and tan 2x.

Ex 2. If and x is in quadrant I, then find sin 2x, cos 2x, and tan 2x.

Class Work 3. If and x is in quadrant II, find sin 2x, cos 2x, and tan 2x.

Half-Angle Formulas

Ex 3. Find the exact value of sin 22.5 .

Ex 4. Find

Ex 5. Find if and u is in quad II.

Class Work 4. Find if and u is in quad IV.

Simplify the expression by using a double-angle or half-angle formula

Product-to-Sum Formulas sin u cos v = ½[sin(u + v) + sin(u – v)] cos u sin v = ½[sin(u + v) – sin(u – v)] cos u cos v = ½[cos(u + v) + cos(u – v)] sin u sin v = ½[cos(u – v) – cos(u + v)]

Ex 6. Express as a sum of trig functions.

Ex 7. Compute sin 15  cos 15 .

Class Work 8. Write the product as a sum. 9. Compute:

Sum-to-Product Formulas

EX 8. Write as a product.

Class Work 10. Write as a product.

HW #2 p odd, odd, odd, odd.