Exam 8: The Unit Circle and Functions of Trigonometry

the formula $s(t)=-9 \cos \frac{\pi}{2} t$ gives the height (in inches) of a weight attached to a spring after $t$ seconds. -Find the maximum height that the weight rises above the equilibrium position of $y=0$ .

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

the formula $s(t)=-11 \cos 5 \pi t$ gives the height (in inches) of a weight attached to a spring after $t$ seconds. -Find the maximum height that the weight rises above the equilibrium position of $y=0$ .

To find the height of a building, a surveyor found that the angle of elevation from a point 42.5 feet from the base of the building is $79^{\circ} 15^{\prime}$ . What is the height of the building?

To find the height of a flagpole, a surveyor found that the angle of elevation from a point 95 feet from the base of the flagpole is $36^{\circ} 40^{\prime}$ . What is the height of the flagpole? .

Find the exact values of each part labeled with a letter.

Find the exact value of $\cot \left(-480^{\circ}\right)$ .

(a) Convert $-240^{\circ}$ to radians. (b) Convert $\frac{7 \pi}{15}$ to degrees.

A jet leaves an airport on a bearing of $\mathrm{N} 47^{\circ} \mathrm{W}$ and travels for 456 miles. It then turns and continues on a bearing of $\mathrm{S} 43^{\circ} \mathrm{W}$ for 381 miles. How far is the jet from the airport?

If $\cos \theta=-\frac{7}{25}$ and $\theta$ is in quadrant III find the values of the other trigonometric functions of $\theta$ .

the formula $s(t)=-11 \cos 5 \pi t$ gives the height (in inches) of a weight attached to a spring after $t$ seconds. -When does the weight reach its maximum height if $t \geq 0$ ?

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=\tan \left(x-\frac{3 \pi}{2}\right)$

Use the figure to find the following: (a) The smallest positive angle coterminal with $\theta$ . (b) The values of $x$ and $y$ . (c) The values of the six trigonometric functions of $\theta$ . (d) The radian measure of $\theta$ .

A wheel is turning at a speed of 200 revolutions per minute. Through how many degrees does a point on the edge of the wheel move in 1.5 seconds?

Use a calculator to approximate $\theta$ to the nearest tenth in the interval $\left[0,90^{\circ}\right]$ , if $\sin \theta=0.9916711624$ .

Use a calculator to approximate the following. (a) $\cos 28^{\circ} 52^{\prime}$ (b) $\cot 52.1896^{\circ}$ (c) $\csc 19.635^{\circ}$

Find the exact value of $\csc \left(570^{\circ}\right)$ .

(a) Convert $300^{\circ}$ to radians. (b) Convert $-\frac{11 \pi}{30}$ to degrees.

A wheel is turning at a speed of 72 revolutions per minute. Through how many degrees does a point on the edge of the wheel move in 0.75 seconds?

If $(2,-6)$ is on the terminal side of angle $\theta$ in standard position, find $\sin \theta, \cos \theta$ , and $\tan \theta$ .