Question 1

Which of the following equations represents a sinusoid with amplitude 3, period $$2\pi$$, and a vertical shift of 1?

Accepted Answer

$$y = 3 \sin(x) + 1$$

Question 2

What is the amplitude of the function $$y = -5 \cos(4x)$$?

Accepted Answer

$$5$$

Question 3

A mass on a spring oscillates with a maximum displacement of 2 cm and completes one cycle in 0.25 seconds. Which equation models this motion if the mass starts at the maximum displacement?

Accepted Answer

$$d(t) = 2 \cos(8\pi t)$$

Question 4

Which transformation describes the graph of $$y = \sin(2x)$$ compared to $$y = \sin(x)$$?

Accepted Answer

A horizontal shrink by a factor of $$\frac{1}{2}$$

Question 5

What is the period of the function $$y = \cos\left(\frac{x}{3}\right)$$?

Accepted Answer

$$6\pi$$

Question 6

If a sinusoidal function has a maximum value of 7 and a minimum value of 1, what is its amplitude?

Accepted Answer

$$3$$

Question 7

Which of the following best describes the symmetry of the cosine function?

Accepted Answer

Even; symmetric with respect to the y-axis

Question 8

A sinusoidal function is given by $$y = 2 \sin\left(\frac{\pi}{3}x\right). $$What is its frequency?

Accepted Answer

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

Question 9

Which of the following is NOT a property of the sine function?

Accepted Answer

It has horizontal asymptotes at $$y = 1$$ and $$y = -1$$

Question 10

A Ferris wheel makes one complete revolution every 40 seconds and has a radius of 15 meters. If a rider starts at the lowest point, which equation models the rider's height above the center as a function of time $$t (in $$seconds)?

Accepted Answer

$$h(t) = 15 \sin\left(\frac{\pi}{20} t - \frac{\pi}{2}\right)$$

Question 11

What is the vertical shift of the sinusoid $$y = 4 \sin(x) - 3$$?

Accepted Answer

$$-3$$

Question 12

Which of the following functions has a phase shift of $$\frac{\pi}{4} to $$the right?

Accepted Answer

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

Question 13

If $$y = 3 \cos(2x) + 1$$, what is the maximum value of the function?

Accepted Answer

$$4$$

Question 14

A sinusoidal function has period $$T$$ and frequency $$f. $$Which equation correctly relates period and frequency?

Accepted Answer

$$f = \frac{1}{T}$$

Question 15

Which of the following best describes simple harmonic motion?

Accepted Answer

Motion modeled by $$d(t) = a \cos(\omega t) or$$ $$d(t) = a \sin(\omega t)$$

Question 16

Given $$y = 2 \sin(x) + 5$$, what is the range of the function?

Accepted Answer

$$[3, 7]$$

Question 17

Which of the following is the general form of a sinusoid?

Accepted Answer

$$y = a \sin(bx + c) + d$$

Question 18

If $$y = -2 \sin(x)$$, which transformation has been applied to the basic sine function?

Accepted Answer

Reflection over the x-axis and vertical stretch by 2

Question 19

A sinusoidal function has amplitude 6, period $$\pi$$, and is modeled by a cosine function. Which equation could represent this function?

Accepted Answer

$$y = 6 \cos(2x)$$

Graphs of Sine and Cosine: Sinusoids – Precalculus Study Notes

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