Question 1

A Ferris wheel has a radius of $$17$$ feet. The wheel is rotating at a rate that completes one revolution every $$12$$ seconds. What is the linear speed of a seat on the Ferris wheel?

Accepted Answer

$$\frac{17\pi}{6} ft/sec$$

Question 2

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

Accepted Answer

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

Question 3

Which of the following is the correct value for $$	an(\arcsin(\frac{1}{3}))$$?

Accepted Answer

$$\frac{1}{\sqrt{8}}$$

Question 4

A ramp rises $$4$$ feet over a horizontal distance of $$15$$ feet. What is the angle of elevation of the ramp, to the nearest degree?

Accepted Answer

$$16^\circ$$

Question 5

Which of the following is an equivalent expression for $$\sin^2$ x + \cos^2$ x$$?

Accepted Answer

$$1$$

Question 6

Find the amplitude, period, and phase shift of $$y = 2\sin(3x - \frac{\pi}{2}).$$

Accepted Answer

Amplitude: $$2$$, Period: $$\frac{2\pi}{3}$$, Phase shift: $$\frac{\pi}{6}$$ right

Question 7

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

Accepted Answer

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

Question 8

A sound wave can be modeled by $$y = 0.5\sin(440\pi t). $$What is the frequency of the wave?

Accepted Answer

$$220 Hz$$

Question 9

Given $$\cos \alpha = -\frac{5}{13}$$ and $$\alpha is in $$Quadrant III, find $$\sin \alpha.$$

Accepted Answer

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

Question 10

A ladder $$20$$ feet long leans against a wall, making an angle of $$65^\circ$$ with the ground. How high up the wall does the ladder reach?

Accepted Answer

$$20\sin 65^\circ$$

Question 11

Which of the following is the equation of a sine function with amplitude $$3$$, period $$\pi$$, and phase shift $$\frac{\pi}{4} to $$the right?

Accepted Answer

$$y = 3\sin(2x - \frac{\pi}{2})$$

Question 12

If $$\sin 	heta = -\frac{7}{25}$$ and $$	heta is in $$Quadrant IV, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{24}{25}$$

Question 13

A point on the unit circle has coordinates $$(-\frac{1}{2}, \frac{\sqrt{3}}{2}). $$What is the corresponding angle in radians?

Accepted Answer

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

Question 14

Which of the following is the correct double-angle identity for $$\sin 2x$$?

Accepted Answer

$$2\sin x \cos x$$

Question 15

A rotating lighthouse beam makes $$5$$ revolutions per minute. What is the angular speed in radians per second?

Accepted Answer

$$\frac{\pi}{6}$$ rad/sec

Question 16

If $$\cos 	heta = 0.6$$ and $$	heta is in $$Quadrant I, what is $$\sin 	heta$$?

Accepted Answer

$$0.8$$

Question 17

A building casts a $$30-$$foot shadow when the angle of elevation of the sun is $$40^\circ. $$How tall is the building?

Accepted Answer

$$30	an 40^\circ$$

Question 18

Which of the following is the correct value for $$\arccos(0)$$?

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

A wheel of radius $$10 cm $$rotates at $$120$$ revolutions per minute. What is the linear speed at the rim in cm/sec?

Accepted Answer

$$40\pi cm/sec$$

Precalculus Trigonometry and Analytic Geometry Study Guide (Ch. 4–4.8)

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