Question 1

Which of the following best describes the amplitude and period of the function $$y = 3 \sin(2x)$$?

Accepted Answer

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

Question 2

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

Accepted Answer

$$\frac{1}{2}$$

Question 3

Which transformation occurs when the function $$y = \sin(x) is $$changed to $$y = -2\sin(x)$$?

Accepted Answer

Vertical stretch by 2 and reflection about the x-axis

Question 4

Given the graph of $$y = \cos(x)$$, what is the y-intercept?

Accepted Answer

1

Question 5

A Ferris wheel is modeled by $$y = 10 \sin\left(\frac{\pi}{6} t\right)$$, where $$t is $$time in seconds. What is the period of one revolution?

Accepted Answer

$$12$$

Question 6

Which of the following statements is true about the sine function $$y = \sin(x)$$?

Accepted Answer

It is an odd function.

Question 7

If $$y = 4 \cos(\frac{\pi}{2} x)$$, what is the amplitude and period?

Accepted Answer

Amplitude: 4, Period: $$4$$

Question 8

A temperature sensor records data that fits the model $$T = 15 + 8 \sin\left(\frac{\pi}{12} t\right)$$, where $$t is $$hours after midnight. What is the maximum temperature predicted by this model?

Accepted Answer

$$23$$

Question 9

Which equation represents a cosine function with amplitude 5 and period $$\pi$$?

Accepted Answer

$$y = 5 \cos(2x)$$

Question 10

A sinusoidal graph has a maximum value of 6, a minimum value of $$-2$$, and a period of $$8. $$What is the equation of the graph if it is a sine function starting at its midline at $$x=0$$?

Accepted Answer

Question 11

Which of the following is the correct range for the function $$y = -3 \sin(x)$$?

Accepted Answer

$$[-3, 3]$$

Question 12

If $$y = 2 \cos(3x)$$, how many complete cycles does the graph make from $$x = 0 to$$ $$x = 2\pi$$?

Accepted Answer

3

Question 13

Which transformation results in the graph of $$y = \sin(x)$$ being reflected about the y-axis?

Accepted Answer

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

Question 14

A sinusoidal function has amplitude 7 and period $$10. $$Which of the following could be its equation?

Accepted Answer

$$y = 7 \sin\left(\frac{\pi}{5} x\right)$$

Question 15

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

Accepted Answer

Even function, symmetric about the y-axis

Question 16

A city’s daylight hours can be modeled by $$D = 12 + 3 \cos\left(\frac{2\pi}{365} t\right)$$, where $$t is $$days after January 1. What is the minimum number of daylight hours predicted?

Accepted Answer

9

Question 17

Which of the following is the period of $$y = \sin\left(\frac{x}{3}\right)$$?

Accepted Answer

$$6\pi$$

Question 18

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

Accepted Answer

$$-2$$

Question 19

A sinusoidal function has a midline at $$y = -1$$, amplitude $$3$$, and period $$4. $$Which equation matches these properties?

Accepted Answer

$$y = 3 \sin\left(\frac{\pi}{2} x\right) - 1$$

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

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