Q: Which of the following is the reciprocal identity for $$\sec \theta$$?

$$\sec \theta = \frac{1}{\cos \theta}$$

Q: Which of the following expressions is equivalent to $$\tan \theta$$ using the quotient identity?

$$\frac{\sin \theta}{\cos \theta}$$

Question 1

A Ferris wheel has a radius of 20 meters. If the wheel rotates through an angle of $$\frac{\pi}{3}$$ radians, what is the length of the arc traveled by a passenger?

Accepted Answer

$$\frac{20\pi}{3}$$ meters

Question 2

Convert $$225^\circ to $$radians.

Accepted Answer

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

Question 3

Given $$\sin 	heta = \frac{3}{5}$$ and $$	heta is in $$Quadrant II, what is $$\cos 	heta$$?

Accepted Answer

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

Question 4

Which of the following is the period of the function $$y = 	an x$$?

Accepted Answer

$$\pi$$

Question 5

Find the exact value of $$\sin\left(\arccos\left(\frac{1}{3}\right)\right).$$

Accepted Answer

Question 6

Which trigonometric functions are positive in Quadrant III?

Accepted Answer

$$	an$$ and $$\cot$$

Question 7

What is the reference angle for $$210^\circ$$?

Accepted Answer

$$30^\circ$$

Question 8

Find the exact value of $$	an\left(\frac{\pi}{4}ight).$$

Accepted Answer

$$1$$

Question 9

Which of the following is a coterminal angle with $$-45^\circ$$?

Accepted Answer

$$315^\circ$$

Question 10

If $$\sin 	heta = \frac{1}{2}$$ and $$	heta is in $$Quadrant II, what is $$	heta in $$radians?

Accepted Answer

$$\frac{5\pi}{6}$$

Question 11

Which identity is equivalent to $$1 + 	an^2$ 	heta$$?

Accepted Answer

$$\sec^2$ 	heta$$

Question 12

A runner completes a circular track of radius 50 meters, running a total angle of $$3\pi$$ radians. What is the total distance run?

Accepted Answer

$$150\pi$$ meters

Question 13

Evaluate $$\cos(390^\circ).$$

Accepted Answer

$$\cos(30^\circ) = \frac{\sqrt{3}}{2}$$

Question 14

Which of the following is the amplitude of $$y = 3\sin x$$?

Accepted Answer

$$3$$

Question 15

Find the exact value of $$\sin\left(\arctan\left(\frac{3}{4}\right)\right).$$

Accepted Answer

$$\frac{3}{5}$$

Question 16

Which of the following is the reciprocal identity for $$\sec 	heta$$?

Accepted Answer

$$\sec 	heta = \frac{1}{\cos 	heta}$$

Question 17

If $$	an 	heta = 2$$ and $$	heta is in $$Quadrant III, what is $$\sin 	heta$$?

Accepted Answer

$$-\frac{2}{\sqrt{5}}$$

Question 18

Which of the following expressions is equivalent to $$	an 	heta$$ using the quotient identity?

Accepted Answer

$$\frac{\sin 	heta}{\cos 	heta}$$

Question 19

Convert $$\frac{7\pi}{6}$$ radians to degrees.

Accepted Answer

$$210^\circ$$

Question 20

If $$\cos 	heta = -\frac{1}{2}$$ and $$	heta is in $$Quadrant III, what is $$	heta in $$degrees?

Accepted Answer

$$210^\circ$$

Comprehensive Study Guide: Trigonometric Functions and Identities

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