91Ó°ÊÓ

State whether or not the equation is an identity. If it is an identity, prove it. $$\cot (-x)=-\cot x$$

Find \(\sin \frac{x}{2}, \cos \frac{x}{2},\) and \(\tan \frac{x}{2}\) under the given conditions. $$\sin x=-\frac{3}{5} \quad\left(\frac{3 \pi}{2}

State whether or not the equation is an identity. If it is an identity, prove it. $$\sec (-x)=\sec x$$

Assume that \(\sin x=.8\) and \(\sin y=\sqrt{.75}\) and that \(x\) and y lie between 0 and \(\pi / 2\). Evaluate the given expressions. $$\cos (x-y)$$

Find the exact functional value without using a calculator. $$\tan ^{-1}(\cos \pi)$$

Find all angles \(\theta\) with \(0^{\circ} \leq \theta<360^{\circ}\) that are solutions of the given equation. IHint: Put your calculator in degree mode and replace \(\pi\) by \(180^{\circ}\) in the solution algorithms for basic equations. \(]\) $$4 \cos ^{2} \theta+4 \cos \theta-3=0$$

Find the exact functional value without using a calculator. $$\sin ^{-1}(\cos 7 \pi / 6)$$

Find all angles \(\theta\) with \(0^{\circ} \leq \theta<360^{\circ}\) that are solutions of the given equation. IHint: Put your calculator in degree mode and replace \(\pi\) by \(180^{\circ}\) in the solution algorithms for basic equations. \(]\) $$\tan ^{2} \theta-3=0$$

Find \(\sin \frac{x}{2}, \cos \frac{x}{2},\) and \(\tan \frac{x}{2}\) under the given conditions. $$\tan x=\frac{1}{2} \quad\left(\pi

State whether or not the equation is an identity. If it is an identity, prove it. $$\sec ^{4} x-\tan ^{4} x=1+2 \tan ^{2} x$$