Question 1

What is the amplitude and period of the function $$y = 3 \sin(2x)$$?

Accepted Answer

Amplitude: $$3$$, Period: $$\pi$$

Question 2

Which of the following best describes the transformation from $$y = \cos x to$$ $$y = 2\cos(3x)$$?

Accepted Answer

Vertical stretch by $$2$$ and horizontal compression by $$\frac{1}{3}$$

Question 3

A sound wave can be modeled by $$y = 0.5 \sin(4\pi t)$$, where $$t is in $$seconds. What is the period of this wave?

Accepted Answer

$$\frac{1}{4}$$ seconds

Question 4

Given the function $$y = -4 \cos(\pi x) - 2$$, what is the range of the function?

Accepted Answer

$$[-6, 2]$$

Question 5

Which of the following points is a maximum for $$y = \sin x$$?

Accepted Answer

$$(\frac{\pi}{2}, 1)$$

Question 6

If $$y = A \sin(\omega x)$$ has amplitude $$5$$ and period $$\frac{2\pi}{3}$$, what is $$\omega$$?

Accepted Answer

$$3$$

Question 7

Which statement is true about the function $$y = \cos x$$?

Accepted Answer

It is an even function.

Question 8

A Ferris wheel is modeled by $$y = 10 \cos(\frac{\pi}{5} t)$$, where $$t is $$time in seconds. What is the period of one revolution?

Accepted Answer

$$10$$ seconds

Question 9

Which equation represents a sine function with amplitude $$4$$ and period $$8$$?

Accepted Answer

Question 10

Which of the following is the correct formula for the period $$T of$$ $$y = A \sin(\omega x)$$?

Accepted Answer

$$T = \frac{2\pi}{\omega}$$

Question 11

If $$y = 2 \sin(2x)$$, what are the $$x-$$coordinates of the five key points for one period starting at $$x = 0$$?

Accepted Answer

$$0, \frac{\pi}{4}, \frac{\pi}{2}, \frac{3\pi}{4}, \pi$$

Question 12

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

Accepted Answer

$$[-2, 2]$$

Question 13

A temperature model is given by $$T = 15 \cos(\frac{\pi}{6} t) + 60. $$What is the maximum temperature predicted by this model?

Accepted Answer

$$75$$

Question 14

Which of the following is equivalent to $$\sin x$$?

Accepted Answer

$$\cos(x - \frac{\pi}{2})$$

Question 15

If $$y = -3 \sin(\frac{\pi}{4} x)$$, what is the amplitude and period?

Accepted Answer

Amplitude: $$3$$, Period: $$8$$

Question 16

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

Accepted Answer

Starts at $$(0, 1)$$ and has a minimum at $$(\pi, -1)$$

Question 17

A sinusoidal function has amplitude $$2$$, period $$\pi$$, and passes through $$(0, 0). $$Which equation could represent this function?

Accepted Answer

$$y = 2 \sin(2x)$$

Question 18

Which of the following is NOT a property of the sine function $$y = \sin x$$?

Accepted Answer

Its maximum value is $$1 at$$ $$x = 0.$$

Graphs of Sine and Cosine Functions: Amplitude, Period, and Transformations

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