91Ó°ÊÓ

Give the degree measure of \(\theta,\) if it exists. Do not use a calculator. $$\theta=\cot ^{-1}\left(-\frac{\sqrt{3}}{3}\right)$$

Use identities to write each expression as a function with \(x\) as the only argument. $$\tan \left(45^{\circ}+x\right)$$

Solve each equation for solutions over the interval \(\left[0^{\circ}, 360^{\circ}\right) .\) Give solutions to the nearest tenth as appropriate. $$9 \sin ^{2} \theta-6 \sin \theta=1$$

Use a half-number (or angle) identity to find an expression for the exact value for each trigonometric function. $$\sin 67.5^{\circ}$$

Use identities to write each expression as a function with \(x\) as the only argument. $$\tan (\pi+x)$$

Give the degree measure of \(\theta,\) if it exists. Do not use a calculator. $$\theta=\sec ^{-1}(-2)$$

Write expression in terms of sine and cosine, and simplify it. (The final expression does not have to be in terms of sine and cosine.) $$\sec \theta \cot \theta \sin \theta$$

Use a half-number (or angle) identity to find an expression for the exact value for each trigonometric function. $$\tan 195^{\circ}$$

Solve each equation for solutions over the interval \(\left[0^{\circ}, 360^{\circ}\right) .\) Give solutions to the nearest tenth as appropriate. $$4 \cos ^{2} \theta+4 \cos \theta=1$$

Use a graphical method to solve each equation over the interval \([0,2 \pi) .\) Round values to the nearest thousandth. $$\sin 3 x-\sin x=0$$