91Ó°ÊÓ

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

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? (figure cannot copy)

Use a sketch to find the exact value of each expression. $$\tan \left(\cos ^{-1} \frac{5}{13}\right)$$

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

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

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. $$y=-4 \cos \left(2 x-\frac{\pi}{2}\right)$$

Express the exact value of each function as a single fraction. Do not use a calculator. $$\text { If } f(\theta)=2 \sin \theta-\sin \frac{\theta}{2}, \text { find } f\left(\frac{\pi}{3}\right)$$.

Use a sketch to find the exact value of each expression. $$\cot \left(\sin ^{-1} \frac{5}{13}\right)$$

Find the exact value of each trigonometric function. Do not use a calculator. $$\sin \left(-\frac{\pi}{4}-2000 \pi\right)$$

A nagpole 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.