Q: A circle has a radius of 18.20 cm. What is the length of the arc intercepted by a central angle of $$\frac{3\pi}{8}$$ radians?

$$s = 18.20 \times \frac{3\pi}{8} = 21.47 cm$$

Q: The area of a sector of a circle with radius $$r$$ and central angle $$\theta (in $$radians) is:

$$A = \frac{1}{2} r^2$ \theta$$

Q: Which of the following is the domain of the tangent function $$y = \tan x$$?

$$\{ x \mid x \neq \frac{\pi}{2} + n\pi,\ n \in \mathbb{Z} \}$$

Q: Which of the following is the correct formula for converting radians to degrees?

$$\text{Degrees} = \text{Radians} \times \frac{180$$^{\circ}$$}{\pi}$$

Question 1

A circle has a radius of 18.20 cm. What is the length of the arc intercepted by a central angle of $$\frac{3\pi}{8}$$ radians?

Accepted Answer

$$s = 18.20 	imes \frac{3\pi}{8} = 21.47 cm$$

Question 2

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

Accepted Answer

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

Question 3

Which of the following is the period of the function $$y = \sin(3x)$$?

Accepted Answer

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

Question 4

A belt runs a pulley of radius 6 cm at 80 revolutions per minute. What is the linear speed of the belt in cm/s?

Accepted Answer

$$v = 16\pi cm/s$$

Question 5

Which of the following angles is coterminal with $$-75^{\circ}$$ and has the smallest positive measure?

Accepted Answer

$$285^{\circ}$$

Question 6

If $$\sin s = \frac{1}{2}$$ and $$s is in $$quadrant II, what is $$\cos s$$?

Accepted Answer

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

Question 7

Which of the following is the amplitude of $$y = -2 \sin(3x)$$?

Accepted Answer

$$2$$

Question 8

The area of a sector of a circle with radius $$r$$ and central angle $$	heta (in $$radians) is:

Accepted Answer

$$A = \frac{1}{2} r^2$ 	heta$$

Question 9

Which of the following is the equation for the vertical translation of $$y = \cos x by 3 $$units upward?

Accepted Answer

$$y = 3 + \cos x$$

Question 10

If $$	heta is in $$standard position and its terminal side lies along the negative $$y-$$axis, which of the following is true?

Accepted Answer

$$	heta = 270$$^{\circ}$$

Question 11

Which of the following is the correct identity for all $$s$$ where $$\cos s 
eq 0$$?

Accepted Answer

$$1 + 	an^2$ s = \sec^2$ s$$

Question 12

Suppose the monthly average temperature in a city is modeled by $$f(x) = 14 \sin\left(\frac{\pi}{6}(x - 4.2)\right) + 68. $$What is the period of this function in months?

Accepted Answer

$$12$$

Question 13

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

Accepted Answer

$$\{ x \mid x 
eq \frac{\pi}{2} + n\pi,\ n \in \mathbb{Z} \}$$

Question 14

If $$\sin x = 0$$, which of the following is true about $$\csc x$$?

Accepted Answer

$$\csc x is $$undefined

Question 15

Which transformation results in the graph of $$y = \sin(x - \frac{\pi}{2})$$ from $$y = \sin x$$?

Accepted Answer

A horizontal translation $$\frac{\pi}{2}$$ units to the right

Question 16

Which of the following is the correct formula for converting radians to degrees?

Accepted Answer

$$	ext{Degrees} = 	ext{Radians} 	imes \frac{180$$^{\circ}$$}{\pi}$$

Question 17

If $$\cos s = 0.5$$ and $$s is in $$quadrant IV, what is $$\sin s$$?

Accepted Answer

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

Question 18

Which of the following describes the graph of $$y = \sec x$$?

Accepted Answer

It has vertical asymptotes at $$x = \frac{\pi}{2} + n\pi$$, period $$2\pi$$, and is an even function.

Question 19

A point $$P$$ moves on a circle of radius 10 cm with angular speed $$\omega = \frac{\pi}{3}$$ radians per second. What is the linear speed of $$P$$?

Accepted Answer

$$\frac{10\pi}{3} cm/s$$

Question 20

Which of the following is the correct equation for a cotangent function with period $$\frac{\pi}{2}$$ and vertical translation 1 unit down?

Accepted Answer

$$y = \cot 2x - 1$$

Chapter 9: The Unit Circle and the Functions of Trigonometry - Precalculus Study Notes

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