Question 1

Which of the following best describes the amplitude and period of the function $$y = -3 \sin(4x)$$?

Accepted Answer

Amplitude: $$3$$, Period: $$\dfrac{\pi}{2}$$

Question 2

A sound wave can be modeled by $$y = 2 \cos(5x). $$What is the maximum value of the wave, and at which $$x-$$value does it first occur?

Accepted Answer

Maximum value: $$2$$, at $$x = 0$$

Question 3

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

Accepted Answer

$$[-4, 4]$$

Question 4

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

Accepted Answer

Vertical stretch by a factor of $$2$$

Question 5

A Ferris wheel is modeled by $$y = 10 \sin\left(\dfrac{\pi}{6}x\right). $$What is the period of the wheel's rotation?

Accepted Answer

$$12$$

Question 6

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

Accepted Answer

It is an even function and has a period of $$2\pi$$

Question 7

If $$y = -2 \sin(\pi x)$$, what is the minimum value of the function and where does it first occur for $$x \geq 0$$?

Accepted Answer

Minimum value: $$-2$$, at $$x = 0.5$$

Question 8

A temperature sensor records data modeled by $$y = 5 \cos\left(\dfrac{\pi}{12}x\right) + 20. $$What is the average temperature over one period?

Accepted Answer

$$20$$

Question 9

Which equation represents a sine function with amplitude $$7$$ and period $$8$$?

Accepted Answer

$$y = 7 \sin\left(\dfrac{\pi}{4}x\right)$$

Question 10

A sinusoidal graph has a maximum value of $$6$$ and a minimum value of $$-2. $$What is the amplitude?

Accepted Answer

$$4$$

Question 11

Which of the following best describes the effect of replacing $$x$$ with $$2x in $$the function $$y = \sin(x)$$?

Accepted Answer

The period is halved

Question 12

Given $$y = -3 \cos(\pi x) + 1$$, what is the range of the function?

Accepted Answer

$$[-2, 4]$$

Question 13

A sinusoidal function has period $$T = 10$$ and amplitude $$A = 2. $$Which equation could represent this function?

Accepted Answer

$$y = 2 \sin\left(\dfrac{2\pi}{10}x\right)$$

Question 14

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

Accepted Answer

It is an odd function and periodic with period $$2\pi$$

Question 15

If the graph of $$y = \cos(x) is $$shifted down $$3$$ units, what is the new equation?

Accepted Answer

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

Question 16

A sinusoidal function is reflected about the $$x-$$axis and has amplitude $$5$$ and period $$6. $$Which equation matches these properties?

Accepted Answer

$$y = -5 \sin\left(\dfrac{2\pi}{6}x\right)$$

Question 17

Which of the following real-world phenomena can be modeled by a sinusoidal function?

Accepted Answer

The height of a point on a rotating Ferris wheel

Question 18

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

Accepted Answer

$$\dfrac{2\pi}{3}$$

Question 19

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

Accepted Answer

$$2$$

Graphs of the Sine and Cosine Functions

Study Guide - Practice Questions