6. Trigonometric Identities and More Equations

Use identities to write each expression in terms of sin θ and cos θ, and then simplify so that no quotients appear and all functions are of θ only.

csc θ - sin θ

Use identities to write each expression in terms of sin θ and cos θ, and then simplify so that no quotients appear and all functions are of θ only.

csc² θ + sec² θ

Perform each indicated operation and simplify the result so that there are no quotients.

sec x/csc x + csc x/sec x

Work each problem.

Given tan x = -5⁄4, where π/2< x < π, use the trigonometric identities to find cot x, csc x and sec x.

Perform each indicated operation and simplify the result so that there are no quotients.

cos β(sec β + csc β)

Work each problem.

Find the exact values of sin x, cos x, and tan x, for x = π/12 , using

a. difference identities

b. half-angle identities. 

Perform each indicated operation and simplify the result so that there are no quotients.

cos x/sec x + sin x/csc x

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

sin 35°

Perform each indicated operation and simplify the result so that there are no quotients.

(tan x + cot x)²

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

-sin 35°

For each expression in Column I, choose the expression from Column II that completes an identity.

2. csc x = ____

Perform each indicated operation and simplify the result so that there are no quotients.

(1 + tan θ)² - 2 tan θ

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

cos 75°

Perform each indicated operation and simplify the result so that there are no quotients.

1/( sin α - 1) - 1/(sin α + 1)

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

sin 300°