Multiple-Angle and Product-to-Sum Formulas (Section 5-5)

Double-Angle Formulas

Example 1 Use the figure to find the exact value. sin x cos x cos 2x sin 2x tan 2x sec 2x csc 2x cot 2x 8 15 17

Find the exact solutions of the equation algebraically on the interval [0, 2π). Example 2

Find the exact solutions of the equation algebraically on the interval [0, 2π). Example 3

Find the exact solutions of the equation algebraically on the interval [0, 2π). Example 4

Find the exact solutions values of sin 2u, cos 2u, and tan 2u using the double-angle formulas. Example 5

Find the exact solutions values of sin 2u, cos 2u, and tan 2u using the double-angle formulas. Example 6

Use a double angle formula to rewrite the expression. Example 7

Use a double angle formula to rewrite the expression. Example 8

Power Reducing Formulas

Rewrite the expression in terms of the first power of cosine. Example 9

Rewrite the expression in terms of the first power of cosine. Example 10

HW #23 pg 394 (1-35odd)

Half-Angle Formulas

Example 11 Use the figure to find the exact value of each trigonometric function. 3 4 5 θ a) b) c) d) e) f)

Example 12 Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle.

Example 13 Find the exact values of the sin (u/2), cos(u/2), and tan(u/2) using the half-angle formulas.

Example 14 Use the half-angle formulas to simplify the expression.

Example 15 Find the solutions of the equation in the interval [0, 2π).

HW #24 pg 395 (37-59odd)

Product-to-Sum Formulas

Use the product-to-sum formulas to write the product as a sum or difference. Example 16

Use the product-to-sum formulas to write the product as a sum or difference. Example 17

Use the product-to-sum formulas to write the product as a sum or difference. Example 18

Sum-to-Product Formulas

Use the sum-to-product formulas to write the sum or difference as a product. Example 19

Use the sum-to-product formulas to write the sum or difference as a product. Example 20

Use the sum-to-product formulas to find the exact value of the expression. Example 21

Find the solutions of the equation in the interval [0, 2π) Example 22

HW #25 pg 395-396 (61-87odd)

Verify the identity algebraically. Example 23

Verify the identity algebraically. Example 24

Verify the identity algebraically. Example 25

Verify the identity algebraically. Example 26

Rewrite the function using the power-reducing formulas. Example 27

Write the trigonometric expression as an algebraic expression. Example 28

HW #26 pg 396 (93-119 odd)