91Ó°ÊÓ

Round answers according to the rounding conventions on page 364. Find the third side of the triangle. $$b=30, c=24, A=120^{\circ}$$

Solve each equation for exact solutions in the interval \(0 \leq x<2 \pi\) $$4 \sin ^{2} x+2 \sqrt{3} \sin x-\sqrt{3}=2 \sin x$$

Find the exact value of the given expression. If an exact value cannot be given, give the value to the nearest ten-thousandth. $$\cos \left(\cos ^{-1} \frac{1}{2}\right)$$

Perform the indicated operations where \(u=\langle-2,4\rangle\) and \(v=\langle-3,-2\rangle\). $$\frac{2}{3} u+\frac{1}{6} v$$

A 12 -foot ladder is resting against a wall and makes an angle of \(52^{\circ}\) with the ground. Find the height to which the ladder will reach on the wall.

Find the exact values of \(\sin 2 \theta, \cos 2 \theta\) and tan \(2 \theta\) given the following information. \(\sin \theta=\frac{8}{17}\) \(\theta\) is in Quadrant II.

Find the exact value of the given expression. If an exact value cannot be given, give the value to the nearest ten-thousandth. $$\tan \left(\tan ^{-1} \frac{1}{2}\right)$$

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

Find the exact values of \(\sin 2 \theta, \cos 2 \theta\) and tan \(2 \theta\) given the following information. \(\sin \theta=-\frac{9}{41}\) \(\theta\) is in Quadrant III.

In Exercises I to \(42,\) verify each identity. $$\sec x=\frac{\cot x+\tan x}{\csc x}$$