91Ó°ÊÓ

Solve each equation for exact solutions in the interval \(0 \leq x<2 \pi\) $$\tan ^{2} x+\tan x-\sqrt{3}=\sqrt{3} \tan x$$

Perform the indicated operations where \(u=\langle-2,4\rangle\) and \(v=\langle-3,-2\rangle\). $$\|\mathbf{u}\|$$

Solve each equation, where \(0^{\circ} \leq x<360^{\circ} .\) Round approximate solutions to the nearest tenth of a degree. $$\cos x-0.75=0$$

Find the exact values of \(\sin 2 \theta, \cos 2 \theta\) and tan \(2 \theta\) given the following information. \(\tan \theta=-\frac{24}{7}\) \(\theta\) is in Quadrant IV.

Find the exact value of the given expression. If an exact value cannot be given, give the value to the nearest ten-thousandth. $$\sin \left(\tan ^{-1} \frac{3}{4}\right)$$

Find the exact values of \(\sin 2 \theta, \cos 2 \theta\) and tan \(2 \theta\) given the following information. \(\tan \theta=\frac{4}{3}\) \(\theta\) is in Quadrant I.

In Exercises I to \(42,\) verify each identity. $$\frac{2 \sin x \cot x+\sin x-4 \cot x-2}{2 \cot x+1}=\sin x-2$$

Solve each equation, where \(0^{\circ} \leq x<360^{\circ} .\) Round approximate solutions to the nearest tenth of a degree. $$\sin x+0.432=0$$

Perform the indicated operations where \(u=\langle-2,4\rangle\) and \(v=\langle-3,-2\rangle\). $$\|\mathbf{v}+2 \mathbf{u}\|$$

Find the exact value of the given expression. If an exact value cannot be given, give the value to the nearest ten-thousandth. $$\cos \left(\sin ^{-1} \frac{5}{13}\right)$$