Question 1

Given the function $$y = 3 \sin\left( \frac{\pi}{2}x - \frac{3\pi}{2} \right) + 1$$, what is the amplitude?

Accepted Answer

$$3$$

Question 2

For the function $$y = 3 \sin\left( \frac{\pi}{2}x - \frac{3\pi}{2} \right) + 1$$, what is the period?

Accepted Answer

$$4$$

Question 3

What is the phase shift of $$y = 3 \sin\left( \frac{\pi}{2}x - \frac{3\pi}{2} \right) + 1$$?

Accepted Answer

$$3$$ units\ to\ the\ right$

Question 4

What is the equation of the midline for $$y = 3 \sin\left( \frac{\pi}{2}x - \frac{3\pi}{2} \right) + 1$$?

Accepted Answer

$$y = 1$$

Question 5

Which of the following is the correct formula for the period of $$y = a \sin(bx + c) + d$$?

Accepted Answer

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

Question 6

A Ferris wheel has a diameter of $$20$$ meters and rotates once every $$40$$ seconds. If a rider starts at the lowest point, which trigonometric function best models the rider's height above the ground over time?

Accepted Answer

$$y = 10 \cos\left( \frac{\pi}{20} t \right) + 10$$

Question 7

If $$y = 2 \sin(3x) - 4$$, what is the midline of the function?

Accepted Answer

$$y = -4$$

Question 8

Which transformation occurs when $$y = \sin(x) is $$changed to $$y = \sin(x - \frac{\pi}{2})$$?

Accepted Answer

A horizontal shift right by $$\frac{\pi}{2}$$

Question 9

Given $$y = -4 \sin(2x) + 5$$, what is the amplitude and midline?

Accepted Answer

Amplitude: $$4$$, Midline: $$y = 5$$

Question 10

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

Accepted Answer

$$\frac{1}{220}$$

Question 11

If the midline of a sinusoidal function is $$y = -2$$ and the amplitude is $$5$$, what are the maximum and minimum values of the function?

Accepted Answer

Maximum: $$3$$, Minimum: $$-7$$

Question 12

Which of the following represents a sine function with amplitude $$2$$, period $$6$$, phase shift $$1$$ unit right, and midline $$y = -3$$?

Accepted Answer

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

Analyzing the Properties of a Sine Function

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