91Ó°ÊÓ

Find the horizontal and vertical components of each vector. Write an equivalent vector in the form \(\mathbf{v}=\mathbf{a}_{1} \mathbf{i}+\mathbf{a}_{2} \mathbf{j}\). Magnitude \(=5,\) direction angle \(=27^{\circ}\)

Find the value of each of the six trigonometric functions for the angle whose terminal side passes through the given point. $$P(2,3)$$

The diagram on the following page shows two ways to play a golf hole. One is to hit the ball down the fairway on your first shot and then hit an approach shot to the green on your second shot. A second way is to hit directly toward the pin. Due to the water hazard, this is a more risky strategy. The distance \(A B\) is 165 yards, \(B C\) is 155 yards, and angle \(A=42.0^{\circ} .\) Find the distance \(A C\) from the tee directly to the pin. Assume that angle \(B\) is an obtuse angle.

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

Find the value of each of the six trigonometric functions for the angle whose terminal side passes through the given point. $$P(3,7)$$

Use a double-angle or half-angle identity to verify the given identity. $$\frac{\cos ^{2} x-\sin ^{2} x}{2 \sin x \cos x}=\cot 2 x$$

Find the horizontal and vertical components of each vector. Write an equivalent vector in the form \(\mathbf{v}=\mathbf{a}_{1} \mathbf{i}+\mathbf{a}_{2} \mathbf{j}\). Magnitude \(=4,\) direction angle \(=127^{\circ}\)

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

Solve each equation, where \(0^{\circ} \leq x<360^{\circ} .\) Round approximate solutions to the nearest tenth of a degree. $$2 \sin ^{2} x=1-\cos x$$

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