Question 1

Convert $$\frac{9\pi}{5}$$ radians to degrees.

Accepted Answer

$$324^\circ$$

Question 2

Convert $$25^\circ to $$radians. Give your answer in terms of $$\pi.$$

Accepted Answer

$$\frac{5\pi}{36}$$

Question 3

Find a positive angle less than $$360^\circ$$ that is coterminal with $$-225^\circ.$$

Accepted Answer

$$135^\circ$$

Question 4

Suppose $$	riangle ABC is a $$right triangle with $$a = 7$$, $$c = 25$$, and right angle at $$C. $$Find the length of side $$b.$$

Accepted Answer

$$24$$

Question 5

Given $$\cos 	heta = -\frac{3}{5}$$ and $$	heta is in $$Quadrant II, find $$\sin 	heta.$$

Accepted Answer

$$\frac{4}{5}$$

Question 6

Use reference angles to find the exact value of $$	an 405^\circ.$$

Accepted Answer

$$1$$

Question 7

Find the reference angle for $$\frac{4\pi}{3}$$ and evaluate $$\cos \frac{4\pi}{3}.$$

Accepted Answer

Reference angle: $$\frac{\pi}{3}$$, $$\cos \frac{4\pi}{3} = -\frac{1}{2}$$

Question 8

Use the unit circle to find $$\sin \frac{21\pi}{4}.$$

Accepted Answer

$$-\frac{\sqrt{2}}{2}$$

Question 9

Determine the amplitude and period of $$y = 4 \sin 2\pi x.$$

Accepted Answer

Amplitude: $$4$$, Period: $$1$$

Question 10

For the function $$y = -3 \cos (4x + \pi)$$, what is the amplitude, period, and phase shift?

Accepted Answer

Amplitude: $$3$$, Period: $$\frac{\pi}{2}$$, Phase shift: $$-\frac{\pi}{4}$$

Question 11

Which of the following is the correct equation for the distance $$d$$ from rest position after $$t$$ seconds for an object on a spring with amplitude $$9$$ inches and period $$2.5$$ seconds, starting downward at $$t=0$$?

Accepted Answer

$$d = -9 \sin \left( \frac{4\pi}{5} t \right)$$

Question 12

A hot-air balloon is rising vertically. The angle of elevation from a point $$124 ft $$from the balloon changes from $$18.4^\circ to$$ $$28.6^\circ. $$How far does the balloon rise during this period (to the nearest tenth of a foot)?

Accepted Answer

$$26.4 ft$$

Question 13

Evaluate $$\sin \left( \sin$$^{-1}$$ \left( -\frac{5\pi}{3} \right) \right). Is $$the expression defined?

Accepted Answer

$$-\frac{\pi}{3}$$

Question 14

Given $$\cos 	heta = -\frac{3}{5}$$ and $$	heta is in $$Quadrant II, find $$	an 	heta.$$

Accepted Answer

$$\frac{4}{3}$$

Question 15

Use a right triangle to find $$\cos \left( \sin$$^{-1}$$ \frac{8}{17} \right). $$Which value is correct?

Accepted Answer

$$\frac{15}{17}$$

Question 16

Use a right triangle to find $$	an \left( \sin$$^{-1}$$ \left( -\frac{8}{10} ight) ight). $$Simplify your answer.

Accepted Answer

$$-\frac{4}{3}$$

Question 17

Find the exact value of $$\sin \left( -\frac{28\pi}{3} \right).$$

Accepted Answer

$$\frac{\sqrt{3}}{2}$$

Question 18

Evaluate $$\cos \left( -\frac{7\pi}{6} \right).$$

Accepted Answer

$$-\frac{\sqrt{3}}{2}$$

Question 19

Which of the following best describes the period of $$y = 	an \left( x - \frac{\pi}{14} ight)$$?

Accepted Answer

$$\pi$$

Question 20

Which of the following is the correct graph for $$y = 8 \csc x$$ over two periods?

Accepted Answer

A graph with vertical asymptotes at $$x = 0, \pi, 2\pi, \ldots$$ and maximum/minimum at $$y = 8$$ and $$y = -8.$$

Precalculus Unit Test TP1 – Step-by-Step Study Guidance

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