Q: A sector of a circle has a radius of 8 cm and a central angle of $$60^\circ. $$What is the area of the sector?

$$\frac{32\pi}{3}$$ \text{ cm}^2$

Q: A medical device rotates through $$270^\circ in 2 $$seconds. What is the angular speed in radians per second?

$$\frac{3\pi}{4}$$ \text{ radians/sec}$

Question 1

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

Accepted Answer

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

Question 2

Which of the following angles is coterminal with $$150^\circ$$?

Accepted Answer

$$-210^\circ$$

Question 3

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

Accepted Answer

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

Question 4

A sector of a circle has a radius of 8 cm and a central angle of $$60^\circ. $$What is the area of the sector?

Accepted Answer

$$\frac{32\pi}{3}$$ 	ext{ cm}^2$

Question 5

Given the point $$(\frac{1}{2}, \frac{\sqrt{3}}{2}) on $$the unit circle, what is $$\sin(	heta)$$?

Accepted Answer

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

Question 6

If a circle has radius $$r = 10$$ and a central angle $$	heta = \frac{\pi}{2}$$ radians, what is the length of the arc?

Accepted Answer

$$5\pi$$

Question 7

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

Accepted Answer

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

Question 8

A sinusoidal function models daylight hours in a city: $$D(t) = 3\sin\left(\frac{\pi}{6}t\right) + 12. $$What is the amplitude of this function?

Accepted Answer

$$3$$

Question 9

What is the period of the function $$y = 2\cos\left(4x\right)$$?

Accepted Answer

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

Question 10

Which equation represents a sine function with amplitude $$5$$, period $$\pi$$, and phase shift $$\frac{\pi}{4} to $$the right?

Accepted Answer

$$y = 5\sin\left(2\left(x - \frac{\pi}{4}\right)\right)$$

Question 11

A medical device rotates through $$270^\circ in 2 $$seconds. What is the angular speed in radians per second?

Accepted Answer

$$\frac{3\pi}{4}$$ 	ext{ radians/sec}$

Question 12

If $$	an(	heta) = 2$$ and $$	heta is in $$quadrant II, what is $$\sin(	heta)$$?

Accepted Answer

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

Question 13

Which of the following is the period of $$y = 	an\left(\frac{1}{2}xight)$$?

Accepted Answer

$$2\pi$$

Question 14

A pendulum swings through an arc of length $$15 cm. If $$the radius is $$10 cm$$, what is the central angle in radians?

Accepted Answer

$$1.5$$

Question 15

If $$y = 4\sin\left(x + \frac{\pi}{3}\right)$$, what is the phase shift?

Accepted Answer

$$-\frac{\pi}{3}$$

Question 16

Which of the following is the equation for the secant function with period $$\pi$$ and vertical shift $$-2$$?

Accepted Answer

$$y = \sec(2x) - 2$$

Question 17

A wheel rotates at $$120$$ revolutions per minute. What is the angular speed in radians per second?

Accepted Answer

$$4\pi$$ 	ext{ radians/sec}$

Question 18

If $$\sin(	heta) = -\frac{1}{2}$$ and $$	heta is in $$quadrant III, what is $$\cos(	heta)$$?

Accepted Answer

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

Question 19

Which transformation will shift the graph of $$y = \sin(x)$$ left by $$\frac{\pi}{2}$$ units?

Accepted Answer

$$y = \sin\left(x + \frac{\pi}{2}\right)$$

Chapter 5: Trigonometric Functions – Review and Applications

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