Practice Amplitude in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Amplitude is the maximum vertical distance from the midline of a periodic function to a peak or trough.

Amplitude is the maximum displacement from the middle of a wave — it is half the total height of a full oscillation from crest to trough.

Showing a random 20 of 50 problems.

Example 1

easy

Find the amplitude of

y = -\cos(x)

Example 2

medium

Find the amplitude of

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

Example 3

hard

Find the amplitude of

y = 7\sin(x) - 24\cos(x)

Example 4

easy

Find the amplitude of

y = 5\sin(3x)

Example 5

easy

Find the amplitude of

y = -6\cos(x)

Example 6

easy

Find the amplitude of

y = 8\sin(x)

Example 7

medium

y = A\sin(x)

has

A > 0

and reaches a max of

11

, find

A

Example 8

medium

A function has midline

y = 2

and reaches a maximum of

11

. Find its amplitude.

Example 9

medium

A sinusoid has midline

y = -2

and amplitude

7

. What are its maximum and minimum values?

Example 10

medium

Find the amplitude of

y = -\frac{3}{4}\sin(2x) - 1

Example 11

challenge

A sinusoid has amplitude

A

, midline

M

. It passes through points

(0, 7)

at maximum and

(2, 1)

at minimum. Find

A

and

M

Example 12

easy

Find the amplitude of

f(x) = 5\sin(x)

Example 13

medium

A sinusoidal function has a maximum value of

8

and a minimum value of

2

. Find the amplitude and midline.

Example 14

easy

A function reaches a maximum of

15

and a minimum of

5

. Find the amplitude.

Example 15

medium

A sinusoid has maximum

12

and minimum

-4

. Find its amplitude.

Example 16

challenge

Two sinusoids of the same period have amplitudes

5

and

12

and are

90°

out of phase. What is the amplitude of their sum?

Example 17

easy

Find the amplitude of

y = -\frac{5}{2}\cos(x) + 3

Example 18

medium

A sinusoid has maximum value

9

and minimum value

1

. Find its amplitude.

Example 19

easy

What is the amplitude of

y = \sin(x)

Example 20

hard

Express

y = 3\sin(x) + 4\cos(x)

R\sin(x + \phi)

and identify the amplitude.

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Related Concepts

Periodic Functions Function Transformation Scaling Functions