Question 1

A point $$(-1, \sqrt{3}) is on $$the terminal side of an angle in standard position. What is the smallest positive angle measure in degrees and radians?

Accepted Answer

$$120^\circ, \ \frac{2\pi}{3}$$

Question 2

Evaluate $$\sin\left(\arccos\left(\frac{1}{2}\right)\right)$$ without a calculator.

Accepted Answer

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

Question 3

Given $$	riangle ABC$$ with $$\angle C = 90^\circ$$, $$a = 12$$, $$c = 13$$, find $$\sin A.$$

Accepted Answer

$$\frac{12}{13}$$

Question 4

A 200 ft guywire is attached to the top of a tower. If the wire makes a $$55^\circ$$ angle with the ground, how tall is the tower?

Accepted Answer

$$200 \sin 55^\circ$$

Question 5

The angle of depression from the top of one building to the foot of a building across the street is $$53^\circ. $$The angle of depression to the top of the same building is $$19^\circ. $$The two buildings are 80 ft apart. What is the height of the shorter building?

Accepted Answer

$$h = H - 80 \left(\cot 19^\circ - \cot 53^\circ\right)$$

Question 6

State the domain and range of one period of $$y = -3 \cos\left(x + \frac{\pi}{2}\right) + 2.$$

Accepted Answer

Question 7

Write an equation for a cosine function with amplitude 6, period $$\pi$$, and phase shift $$\frac{\pi}{4} to $$the left.

Accepted Answer

$$y = 6 \cos\left(2x + \frac{\pi}{2}\right)$$

Question 8

The point $$(-5, -3) is on $$the terminal side of angle $$	heta. $$What is $$\sin 	heta$$?

Accepted Answer

$$-\frac{3}{\sqrt{34}}$$

Question 9

Find the exact value of $$x if$$ $$	an x = -1$$, $$0 \leq x \leq \pi.$$

Accepted Answer

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

Question 10

Describe the end behavior of $$f(x) = \frac{\sin x}{x} as$$ $$x 	o \infty.$$

Accepted Answer

$$f(x) 	o 0$$

Question 11

Evaluate $$\cos$$^{-1}$$\left(\frac{1}{2}\right).$$

Accepted Answer

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

Question 12

Evaluate $$\sin$$^{-1}$$\left(-\frac{1}{2}\right).$$

Accepted Answer

$$-\frac{\pi}{6}$$

Question 13

What is the period and amplitude of $$y = -2 \cos(x + \pi)$$?

Accepted Answer

Period: $$2\pi$$, Amplitude: $$2$$

Question 14

Which of the following is the correct equation for a sine function with amplitude 3, period $$4\pi$$, and vertical shift up 2?

Accepted Answer

$$y = 3 \sin\left(\frac{1}{2}x\right) + 2$$

Question 15

If $$y = \sec(x - \pi)$$, what is the period of the function?

Accepted Answer

$$2\pi$$

Question 16

Evaluate $$	an$$^{-1}$$(\sqrt{3}).$$

Accepted Answer

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

Question 17

A right triangle has legs of length 7 and 24. What is the length of the hypotenuse?

Accepted Answer

$$25$$

Question 18

Which of the following is the correct amplitude and period for $$y = \sin\left(x + \frac{\pi}{2}\right)$$?

Accepted Answer

Amplitude: $$1$$, Period: $$2\pi$$

Question 19

If $$y = \cos 2x + 1$$, what is the range of the function?

Accepted Answer

Unit 4 Test Review: Trigonometric Functions – Study Notes

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