Exam 6: Trigonometric Identities, Inverses, and Equations

Use a double-angle identity to find the exact value.

Evaluate without using a calculator. Answer in radians.

Find the exact values for sin $\theta$ , cos $\theta$ , and tan $\theta$ .

Evaluate. Answer in exact form.

Rewrite the sum as a product using a sum-to-product identity.

Find all solutions in [0, 2 $\pi$ ). -27 tan² x = -9

Find all real solutions. Answer in the exact form. Note that identities are not required to solve this exercise. -12 sin x = 6

Find the exact value.

Rewrite as a single expression.

Find the exact value using a sum-to-product identity.

Use the following to answer questions : tan $\theta$ = ; $\theta$ in QII. -Find the exact value of tan(2 $\theta$ ).

Find the exact value using a sum or difference identity. Some simplifications may involve using symmetry and the formulas for negatives.

Show that the equation is not an identity.

Verify that the equation is an identity.

Find the principal root of the equation. 9 csc x = -18

Use the following to answer questions : $\alpha$ and $\beta$ are acute angles with tan( $\alpha$ ) = and sec( $\beta$ ) = . -Find tan( $\alpha$ + $\beta$ ).

Use the following to answer questions : tan $\theta$ = ; $\theta$ in QII. -Find the exact value of cos(2 $\theta$ ).

Solve the equation in [0, 2π) using identities.

Use the following to answer questions : -Use a half-angle identity to find the exact value of cos $\theta$ .

Rewrite as a single expression. cos(6 $\theta$ )cos(2 $\theta$ ) + sin(6 $\theta$ )sin(2 $\theta$ )