91Ó°ÊÓ

In Exercises \(35-60,\) find the reference angle for each angle. $$-359^{\circ}$$

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. $$y=\frac{1}{2} \cos (2 x+\pi)$$

A building that is 250 feet high casts a shadow 40 feet long. Find the angle of elevation, to the nearest tenth of a degree, of the Sun at this time.

In Exercises \(47-62,\) use a sketch to find the exact value of each expression. $$\tan \left(\cos ^{-1} \frac{5}{13}\right)$$

Express the exact value of each function as a single fraction. Do not use a calculator. $$\text { If } f(\theta)=2 \cos \theta-\cos 2 \theta, \text { find } f\left(\frac{\pi}{6}\right)$$

Find the exact value of each trigonometric function. Do not use a calculator. $$\sin \left(-\frac{\pi}{4}-1000 \pi\right)$$

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. $$y=-3 \cos \left(2 x-\frac{\pi}{2}\right)$$

A hot-air balloon is rising vertically. From a point on level ground 125 feet from the point directly under the passenger compartment, the angle of elevation to the ballon changes from \(19.2^{\circ}\) to \(31.7^{\circ} .\) How far, to the nearest tenth of a foot, does the balloon rise during this period?

A flagpole is situated on top of a building. The angle of elevation from a point on level ground 330 feet from the building to the top of the flagpole is \(63^{\circ} .\) The angle of elevation from the same point to the bottom of the flagpole is \(53^{\circ} .\) Find the height of the flagpole to the nearest tenth of a foot.

Graph two periods of each function. $$y=\sec |x|$$