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

$$v = 20 \times \frac{2\pi}{2} = 20\pi$$ meters/min$

Q: A central angle in a circle of radius 10 cm intercepts an arc of length 8 cm. What is the measure of the angle in radians?

$$\theta = \frac{8}{10} = 0.8$$ radians

Q: If $$y = 2 \sin(3x - \frac{\pi}{2}) + 1$$, what is the phase shift?

$$\frac{\pi}{6}$$ units$$\ \text{right}$$

Q: A wheel rotates at an angular speed of $$\omega = 5$$ radians per second. If the radius is 0.4 meters, what is the linear speed?

$$v = 0.4 \times 5 = 2$$ meters/second

Question 1

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

Accepted Answer

$$v = 20 	imes \frac{2\pi}{2} = 20\pi$$ meters/min$

Question 2

Convert an angle of $$225^\circ to $$radians.

Accepted Answer

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

Question 3

A central angle in a circle of radius 10 cm intercepts an arc of length 8 cm. What is the measure of the angle in radians?

Accepted Answer

$$	heta = \frac{8}{10} = 0.8$$ radians

Question 4

Which of the following is the amplitude of the function $$y = -3 \sin(2x) + 1$$?

Accepted Answer

$$3$$

Question 5

Find the period of the function $$y = \cos\left(\frac{x}{3}\right).$$

Accepted Answer

$$6\pi$$

Question 6

A ladder leans against a wall, forming a $$65^\circ$$ angle with the ground. If the ladder is 10 ft long, how high up the wall does it reach? (Round to two decimal places.)

Accepted Answer

$$10 \sin(65^\circ) \approx 9.06 ft$$

Question 7

Given the point $$P=(-3,4) on $$the terminal side of an angle $$	heta$$, find $$\sin 	heta.$$

Accepted Answer

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

Question 8

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

Accepted Answer

$$30^\circ$$

Question 9

If $$\sin 	heta = \frac{5}{13}$$ and $$	heta is in $$Quadrant II, what is $$\cos 	heta$$?

Accepted Answer

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

Question 10

A pendulum swings according to $$d = 7 \cos(3t). $$What is the period of the motion?

Accepted Answer

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

Question 11

Find all angles coterminal with $$-45^\circ$$ between $$0^\circ$$ and $$360^\circ.$$

Accepted Answer

$$315^\circ$$

Question 12

Which of the following is the correct formula for the period of $$y = 	an(2x)$$?

Accepted Answer

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

Question 13

If $$	an 	heta = -1$$ and $$	heta is in $$Quadrant IV, what is $$	heta in $$radians?

Accepted Answer

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

Question 14

A point on the unit circle corresponding to $$	heta = \frac{2\pi}{3} is$$:

Accepted Answer

$$\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$$

Question 15

If $$y = 2 \sin(3x - \frac{\pi}{2}) + 1$$, what is the phase shift?

Accepted Answer

$$\frac{\pi}{6}$$ units$$\ 	ext{right}$$

Question 16

Which of the following is the reciprocal of $$\sin 	heta$$?

Accepted Answer

$$\csc 	heta$$

Question 17

A wheel rotates at an angular speed of $$\omega = 5$$ radians per second. If the radius is 0.4 meters, what is the linear speed?

Accepted Answer

$$v = 0.4 	imes 5 = 2$$ meters/second

Question 18

If $$\cos 	heta = -\frac{3}{5}$$ and $$	heta is in $$Quadrant III, what is $$\sin 	heta$$?

Accepted Answer

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

Question 19

Which calculator mode should you use to evaluate $$\sin(120^\circ)$$?

Accepted Answer

DEG

Question 20

If $$y = \sec x$$, where will the vertical asymptotes occur?

Accepted Answer

Where $$\cos x = 0$$

Trigonometric Functions and Their Applications: Study Notes

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