91Ó°ÊÓ

Simplify the given expression. $$\text { If } \cos x=-\frac{1}{5} \text { and } \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. \(]\) $$\cos \theta=-.42$$

Find \(\sin \frac{x}{2}, \cos \frac{x}{2},\) and \(\tan \frac{x}{2}\) under the given conditions. $$\cos x=.4 \quad\left(0

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. \(]\) $$\cot \theta=-2.4$$

Simplify the given expression. $$\text { If } \sin x=-\frac{3}{4} \text { and } \frac{3 \pi}{2}

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

Find \(\sin \frac{x}{2}, \cos \frac{x}{2},\) and \(\tan \frac{x}{2}\) under the given conditions. $$\sin x=.6 \quad\left(\frac{\pi}{2}

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

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. $$\sin (x+y)$$

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}