Question 1

Given the equation $$y = a \sin(bx)$$, which parameter affects the period of the sine function?

Accepted Answer

The parameter $$b$$

Question 2

If the amplitude of $$y = 3 \sin(x) is $$changed to $$y = 5 \sin(x)$$, what happens to the graph?

Accepted Answer

The graph stretches vertically

Question 3

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

Accepted Answer

$$\pi$$

Question 4

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

Accepted Answer

Vertical shift upward by 2 units

Question 5

A sound wave can be modeled by $$y = 0.5 \sin(4x). $$What is the amplitude and period of this wave?

Accepted Answer

Amplitude: $$0.5$$, Period: $$\frac{\pi}{2}$$

Question 6

If $$y = \sin(x) is $$reflected over the x-axis, what is the new equation?

Accepted Answer

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

Question 7

Which of the following equations represents a sine function with amplitude 2 and period $$\pi$$?

Accepted Answer

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

Question 8

A Ferris wheel rotates such that the height of a seat above the ground can be modeled by $$y = 10 \sin(\frac{\pi}{6} t) + 12. $$What is the maximum height reached?

Accepted Answer

$$22$$

Question 9

Which graph transformation occurs when $$y = \sin(x)$$ becomes $$y = \sin(x - \frac{\pi}{2})$$?

Accepted Answer

Horizontal shift to the right by $$\frac{\pi}{2}$$

Question 10

If $$y = \sin(x) is $$compressed horizontally by a factor of 3, what is the new equation?

Accepted Answer

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

Question 11

A medical device uses a sine wave with equation $$y = 2 \sin(\frac{\pi}{4} t). $$What is the period of the wave?

Accepted Answer

$$8$$

Question 12

Which equation represents a sine function with a vertical shift downward by 3 units?

Accepted Answer

$$y = \sin(x) - 3$$

Question 13

If the equation $$y = \sin(x) is $$changed to $$y = \sin(2x) + 1$$, which transformations have occurred?

Accepted Answer

Horizontal compression and vertical shift upward

Question 14

A sound engineer models a wave as $$y = 4 \sin(x - \frac{\pi}{3}). $$What is the phase shift?

Accepted Answer

$$\frac{\pi}{3} to $$the right

Question 15

Which of the following best describes the effect of increasing the value of $$b in$$ $$y = \sin(bx)$$?

Accepted Answer

The graph completes more cycles in the same interval

Special Angle/Reference Triangles and Trigonometric Functions

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