91Ó°ÊÓ

$$\text {use a calculator to find the value of the acute}\text { angle } \theta \text { in radians, rounded to three decimal places.}$$ $$\tan \theta=0.4169$$

Determine the amplitude and period of each function. Then graph one period of the function. $$y=-\frac{1}{2} \cos \frac{\pi}{3} x$$

The tallest television transmitting tower in the world is in North Dakota. From a point on level ground 5280 feet (1 mile) from the base of the tower, the angle of elevation is \(21.3^{\circ} .\) Approximate the height of the tower to the nearest foot.

Find the exact value of each trigonometric function. Do not use a calculator. $$\sin \left(-\frac{9 \pi}{4}\right)$$

In Exercises \(35-60\), find the reference angle for each angle. $$\frac{7 \pi}{4}$$

Find the exact value of each expression, if possible. Do not use a calculator. $$\tan ^{-1}\left(\tan \frac{2 \pi}{3}\right)$$

From a point on level ground 30 yards from the base of a building, the angle of elevation is \(38.7^{\circ} .\) Approximate the height of the building to the nearest foot.

Determine the amplitude and period of each function. Then graph one period of the function. $$y=-\frac{1}{2} \cos \frac{\pi}{4} x$$

Graph two periods of the given cosecant or secant function. $$y=\csc \left(x-\frac{\pi}{2}\right)$$

Find the exact value of each trigonometric function. Do not use a calculator. $$\sec \left(-\frac{9 \pi}{4}\right)$$