Transforming Sine and Cosine Graphs

High School Math based on the topics required for the Regents Exam conducted by NYSED.

The following diagram shows how to transform sine and cosine graphs. Scroll down the page for more examples and solutions on how to graph sine and cosine functions.

 

Graphing Sine and Cosine With Different Coefficients (Amplitude and Period)
Examples:
State the amplitude and period of each of the following functions.
a) y = -4 cos (3x)
b) y = 1/2 sin x
c) y = √2 cos(1/2 x)

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Trigonometric Functions and Graphing: Amplitude, Period, Vertical and Horizontal Shifts
Examples:
Graph y = 2 cos (x - π/2) + 1

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Graphing Sine and Cosine with Phase (Horizontal) Shifts
Examples:
What is the phase shift for each of the following functions
a) y = cos(x - 4)
b) y = sin (2(x + 1))
c) y = cos(10x + 30)

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An Introduction to the Graphs of Sine and Cosine Functions

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