Question 1

Convert $$\frac{7\pi}{10}$$ radians to degrees. Round your answer to three decimal places.

Accepted Answer

$$126.000^\circ$$

Question 2

Convert $$72^\circ to $$radians. Write your answer as an exact value using $$\pi.$$

Accepted Answer

$$\frac{2\pi}{5}$$

Question 3

Given $$	heta = \frac{5\pi}{11}$$, which of the following is a positive coterminal angle?

Accepted Answer

$$\frac{5\pi}{11} + 2\pi$$

Question 4

A slice of pizza has a radius of 7 inches and an arc length of 4 inches. What is the angle $$	heta of $$the slice in radians?

Accepted Answer

$$\frac{4}{7}$$

Question 5

Refer to the first triangle image. What is $$\sin	heta$$?

Accepted Answer

$$\frac{\sqrt{14^2$-11^2$$}}{14}$

Question 6

An extension ladder is 15 feet long and makes a $$70^\circ$$ angle with the ground. How high is the top of the ladder above the ground? (Round to two decimal places.)

Accepted Answer

$$15 \sin 70^\circ$$

Question 7

Given the point $$(-3, -2) on $$the terminal side of angle $$	heta ($$see image 6), what is $$\sin	heta$$?

Accepted Answer

$$-\frac{2}{\sqrt{13}}$$

Question 8

What is the amplitude of the function $$f(t) = 4\cos\left(\frac{\pi}{3}t - 4\right) + 1$$?

Accepted Answer

$$4$$

Question 9

What is the period of the function $$f(t) = 4\cos\left(\frac{\pi}{3}t - 4\right) + 1$$?

Accepted Answer

$$\frac{2\pi}{\frac{\pi}{3}}$$

Question 10

Refer to the fourth image (sinusoidal graph). What is the amplitude of the function shown?

Accepted Answer

$$8$$

Question 11

Refer to the fifth image (triangle with sides 7 and 11). What is $$\alpha to $$three decimal places?

Accepted Answer

$$\arctan\left(\frac{7}{11}\right) \approx 32.471^\circ$$

Question 12

What is the range of $$\arcsin(x) in $$radians?

Accepted Answer

$$\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$$

Question 13

Simplify $$\csc^2$	heta - \cot^2$	heta$$ using trigonometric identities.

Accepted Answer

$$1$$

Question 14

Which of the following is a vertical asymptote of $$y = 	an	heta$$ between $$-2\pi$$ and $$2\pi$$?

Accepted Answer

$$	heta = -\frac{3\pi}{2}$$

Question 15

Use identities to simplify $$\cos	heta \sin(-	heta).$$

Accepted Answer

$$-\cos	heta \sin	heta$$

Question 16

Verify the identity: $$(\sec	heta - 1)(\sec	heta + 1) = \frac{\sin^2$	heta}{1 - \sin^2$	heta}. $$What is the first step in the verification?

Accepted Answer

Expand the left side using the difference of squares.

Question 17

Given $$	an	heta = -\frac{28}{45}$$ and $$\sec	heta \u003c 0$$, what is the sign of $$\sin	heta$$?

Accepted Answer

Negative

Question 18

Which of the following is the equation of the midline for $$f(t) = 4\cos\left(\frac{\pi}{3}t - 4\right) + 1$$?

Accepted Answer

$$y = 1$$

Question 19

If $$	heta is in $$standard position and its terminal side passes through $$(-3, -2)$$, what are the coordinates where the terminal side intersects the unit circle?

Accepted Answer

$$\left(\frac{-3}{\sqrt{13}}, \frac{-2}{\sqrt{13}}\right)$$

Right Triangle Trigonometry: Finding Side Lengths

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