Amplitude, Math Dictionary

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Range Periodic Function Bounded range

Amplitude
Definition of Amplitude

Amplitude is half the distance between the minimum and maximum values of the range of a periodic function with a bounded range.
In other words, for functions of the form y = A sin bθ or y = A cos bθ, the amplitude is |A|.

Examples of Amplitude

Solved Example on Amplitude

Find the amplitude of the function .
Choices:
A. - 4
B. 4
C.
D. - 3
Correct Answer: B
Solution:
Step 1: Recall that “for functions of the form y = A cos bθ, the amplitude is |A|.”
Step 2: So, 4 is the amplitude of the given function.

Related Terms for Amplitude

Periodic Function
Range
Function
Bounded

Additional Links for Amplitude

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Browse for solved examples below on this Math Dictionary term:

Alabama Assessment Curriculum - 2006 > Algebra - 2 > Algebra II with Trigonometry > 9-Graph trigonometric functions of the form y=a sin(bx), y=a cos(bx), and y=a tan(bx). Determining period and amplitude of sine, cosine, and tangent functions from graphs or basic equations. Determining specific unit circle coordinates associated with special angles.

Alabama Assessment Curriculum - 2006 > Algebra 2 > Algebra II with Trigonometry > 9-Graph trigonometric functions of the form y=a sin(bx), y=a cos(bx), and y=a tan(bx). Determining period and amplitude of sine, cosine, and tangent functions from graphs or basic equations. Determining specific unit circle coordinates associated with special angles.

Alabama Assessment Curriculum - 2006 > Pre-Calculus > Precalculus > 5-Analyze the effects of parameter changes on the graphs of trigonometric, logarithmic, and exponential functions. Determining the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses.

North Carolina Assessment Curriculum - 2006 > Pre-Calculus > The learner will use relations and functions to solve problems. > 2.02.b-Use trigonometric and inverse trigonometric functions to model and solve problems; justify results. Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.

New York Assessment Curriculum - 2006 > Algebra - 2 > Algebra > A2.A.69-Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function.

New York Assessment Curriculum - 2006 > Algebra 2 > Algebra > A2.A.69-Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function.

Indiana Assessment Curriculum - 2006 > Pre-Calculus > Trigonometric Functions > PC.4.7-Draw and analyze graphs of translations of trigonometric functions, including period, amplitude, and phase shift.

UT Assessment Curriculum - 2006 > Algebra - 2 > Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling. > 3.2.8-Specify locations and describe spatial relationships using coordinate geometry: Perform transformation on the sine and cosine functions involving amplitude, period, phase shift, vertical shift, and reflections.

UT Assessment Curriculum - 2006 > Algebra 2 > Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling. > 3.2.8-Specify locations and describe spatial relationships using coordinate geometry: Perform transformation on the sine and cosine functions involving amplitude, period, phase shift, vertical shift, and reflections.

Arkansas Assessment Curriculum - 2006 > Pre-Calculus > Trigonometric Functions: Students will use different perspectives to develop and apply the definitions of the six trigonometric functions. They will sketch and analyze graphs, find inverse functions, and solve real world problems. > TF.5.PCT.7-Graph the six trigonometric functions, identify domain, range, intercepts, period, amplitude, and asymptotes as applicable and use symmetry to determine whether the function is even or odd through appropriate technology when needed.

Arkansas Assessment Curriculum - 2006 > Pre-Calculus > Trigonometric Functions: Students will use different perspectives to develop and apply the definitions of the six trigonometric functions. They will sketch and analyze graphs, find inverse functions, and solve real world problems. > TF.5.PCT.8-Determine, with and without appropriate technology, the amplitude, period, phase shift, and vertical shift, and sketch the graph of transformations of the trigonometric functions.

ICSE Math Framework > > Complex Numbers > Amplitude of a Complex Number

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