Q: Which of the following is the correct domain for the function $$y = \sec x$$?

$$x \neq \dfrac{\pi}{2} + k\pi$$, where $$k is $$any integer

Question 1

A central angle in a circle of radius $$10 cm $$intercepts an arc of length $$5\pi cm. $$What is the measure of the angle in degrees?

Accepted Answer

$$90^\circ$$

Question 2

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

Accepted Answer

$$\dfrac{5\pi}{4}$$

Question 3

A Ferris wheel with a radius of $$20$$ meters completes one revolution every $$2$$ minutes. What is the linear speed (in meters per minute) of a seat on the edge?

Accepted Answer

$$20\pi$$

Question 4

Which of the following angles is coterminal with $$-120^\circ$$?

Accepted Answer

$$240^\circ$$

Question 5

Given $$\sin 	heta = -\dfrac{3}{5}$$ and $$	heta is in $$Quadrant IV, what is $$\cos 	heta$$?

Accepted Answer

$$\dfrac{4}{5}$$

Question 6

What is the period of the function $$f(x) = 2\sin\left(3x - \dfrac{\pi}{2}\right)$$?

Accepted Answer

$$\dfrac{2\pi}{3}$$

Question 7

Which of the following statements is true about the tangent function $$y = 	an x$$?

Accepted Answer

It is an odd function with period $$\pi.$$

Question 8

Find the amplitude and phase shift of $$f(x) = -3\cos\left(2x + \dfrac{\pi}{3}\right).$$

Accepted Answer

Amplitude: $$3$$, Phase shift: $$-\dfrac{\pi}{6}$$

Question 9

If the point $$P(-\dfrac{1}{2}, -\dfrac{\sqrt{3}}{2})$$ lies on the unit circle, what is $$\sin 	heta$$ for the corresponding angle $$	heta$$?

Accepted Answer

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

Question 10

A sector of a circle has a radius of $$8 cm $$and a central angle of $$\dfrac{\pi}{3}$$ radians. What is the area of the sector?

Accepted Answer

$$\dfrac{32\pi}{3} cm$^2$$

Question 11

Which of the following is the reference angle for $$210^\circ$$?

Accepted Answer

$$30^\circ$$

Question 12

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

Accepted Answer

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

Question 13

Which of the following is the correct domain for the function $$y = \sec x$$?

Accepted Answer

$$x 
eq \dfrac{\pi}{2} + k\pi$$, where $$k is $$any integer

Question 14

A rotating machine part spins at $$120$$ revolutions per minute. What is its angular speed in radians per second?

Accepted Answer

$$4\pi$$ radians/second

Question 15

Which of the following is an even trigonometric function?

Accepted Answer

$$\cos x$$

Question 16

Find the equation of a sine function with amplitude $$2$$, period $$\pi$$, and phase shift $$\dfrac{\pi}{4} to $$the right.

Accepted Answer

$$y = 2\sin\left(2x - \dfrac{\pi}{2}\right)$$

Question 17

If $$\cos 	heta = 0$$ and $$0 \leq 	heta \u003c 2\pi$$, what are all possible values of $$	heta$$?

Accepted Answer

$$\dfrac{\pi}{2}, \dfrac{3\pi}{2}$$

Question 18

A pendulum swings through an angle of $$60^\circ in a $$circle of radius $$1.5$$ meters. What is the length of the arc traced by the pendulum?

Accepted Answer

$$\dfrac{\pi}{2}$$ meters

Question 19

Which of the following is the range of the function $$y = \csc x$$?

Accepted Answer

$$(-\infty, -1] \cup [1, \infty)$$

Question 20

If $$\sin x = \dfrac{1}{2}$$ and $$0 \leq x \u003c 2\pi$$, what are all possible values of $$x$$?

Accepted Answer

$$\dfrac{\pi}{6}, \dfrac{5\pi}{6}$$

Trigonometric Functions and Their Properties: Study Notes for Precalculus

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