91Ó°ÊÓ

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.) $$\frac{\cot ^{2} \theta}{\csc ^{2} \theta}$$

Solve each equation for solutions over the interval \(\left[0^{\circ}, 360^{\circ}\right) .\) Give solutions to the nearest tenth as appropriate. $$\sin ^{2} \theta-2 \sin \theta+3=0$$

Use a half-number identity to find an expression for the exact value for each function, given the information about \(x\). $$\tan \frac{x}{2}, \text { given } \sin x=\frac{3}{5} \text { and } \frac{\pi}{2} < x < \pi$$

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

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

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.) $$\frac{\tan ^{2} \theta}{\sec ^{2} \theta}$$

Use identities to write each expression as a finction with \(x\) as the only argument. $$\tan \left(x+\frac{7 \pi}{4}\right)$$

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

Use a half-number identity to find an expression for the exact value for each function, given the information about \(x\). $$\cos \frac{x}{2}, \text { given } \sin x=-\frac{4}{5} \text { and } \frac{3 \pi}{2} < x < 2 \pi$$

Use a half-number identity to find an expression for the exact value for each function, given the information about \(x\). $$\tan \frac{x}{2}, \text { given } \tan x=\frac{\sqrt{7}}{3} \text { and } \pi < x < \frac{3 \pi}{2}$$