Exam 8: The Unit Circle and Functions of Trigonometry

graph the given function over a two-period interval. Identify asymptotes when applicable - $y=-\cos 2 x$

Use a calculator to approximate the following. (a) $\tan 145^{\circ} 23^{\prime}$ (b) $\sin 38.251^{\circ}$ (c) $\sec 18.563^{\circ}$

graph the given function over a two-period interval. Identify asymptotes when applicable - $y=\tan (x+\pi)$

To find the height of a fence in a baseball park, a groundskeeper found that the angle of elevation from a point 25.5 meters from the base of the fence is $23^{\circ} 54^{\prime}$ . What is the height of the fence?

A jet leaves an airport on a bearing of $\mathrm{S} 29^{\circ} \mathrm{W}$ and travels for 245 miles. It then turns and continues on a bearing of $\mathrm{N} 61^{\circ} \mathrm{W}$ for 506 miles. How far is the jet from the airport?

(a) Convert $-225^{\circ}$ to radians. (b) Convert $\frac{3 \pi}{10}$ to degrees.

A central angle of a circle with radius 50 centimeters cuts off an arc of 80 centimeters. Find each measure. (a) The radian measure of the angle. (b) The area of the sector with this central angle.

A jet leaves an airport on a bearing of $\mathrm{S} 37^{\circ} \mathrm{E}$ and travels for 324 miles. It then turns and continues on a bearing of $\mathrm{N} 53^{\circ} \mathrm{E}$ for 215 miles. How far is the jet from the airport?

the formula $s(t)=-5 \cos 3 \pi t$ gives the height (in inches) of a weight attached to a spring after $t$ seconds. -When does the weight reach its maximum height if $t \geq 0$ ?

Find the exact value of $\cot \left(-765^{\circ}\right)$ .

Solve the triangle.

If $\sin \theta=\frac{3}{5}$ and $\theta$ is in quadrant II find the values of the other trigonometric functions of $\theta$ .

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=\tan (x-\pi)$

Find the length of an arc intercepted by an angle of $60^{\circ}$ in a circle with radius 15 inches.

If $(-3,4)$ is on the terminal side of an angle $\theta$ in standard position, find $\sin \theta, \cos \theta$ , and $\tan \theta$ .

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=-\sin 2 x$

Use a calculator to approximate the following. (a) $\sin 29^{\circ} 8^{\prime}$ (b) $\cot 95.598^{\circ}$ (c) $\sec 142.199^{\circ}$

Solve the triangle.

Use a calculator to approximate $\theta$ in the interval $\left[0,90^{\circ}\right]$ , if $\sin \theta=0.7313537016$ .

If $\csc \theta>0$ and $\sec \theta<0$ , in which quadrant does $\theta$ lie?