91Ó°ÊÓ

Find the exact value of the given expression. If an exact value cannot be given, give the value to the nearest ten-thousandth. $$\sin \left[\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right]$$

Find the exact values of \(\sin \frac{\alpha}{2}, \cos \frac{\alpha}{2}\) and tan \(\frac{\alpha}{2}\) given the following information. $$\sin \alpha=-\frac{7}{25} \quad \alpha \text { is in Quadrant III. }$$

Solve each equation, where \(0^{\circ} \leq x<360^{\circ} .\) Round approximate solutions to the nearest tenth of a degree. $$4 \cos x-1=0$$

Solve each equation, where \(0^{\circ} \leq x<360^{\circ} .\) Round approximate solutions to the nearest tenth of a degree. $$3 \sec x-8=0$$

Perform the indicated operations where \(u=3 i-2 j\) and \(v=-2 i+3 j\). $$4 \mathbf{v}$$

Find the exact values of \(\sin \frac{\alpha}{2}, \cos \frac{\alpha}{2}\) and tan \(\frac{\alpha}{2}\) given the following information. $$\cos \alpha=-\frac{8}{17} \quad \alpha \text { is in Quadrant III. }$$

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

Round answers according to the rounding conventions on page 364. Given three sides of a triangle, find the specified angle. $$a=25, b=32, c=40 ; \text { find } A$$

In Exercises I to \(42,\) verify each identity. $$\sin ^{2} x-\cos ^{2} x=2 \sin ^{2} x-1$$

Find the exact values of \(\sin \frac{\alpha}{2}, \cos \frac{\alpha}{2}\) and tan \(\frac{\alpha}{2}\) given the following information. $$\cos \alpha=\frac{12}{13} \quad \alpha \text { is in Quadrant I. }$$