Transforming Sine and Cosine Graphs

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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.

Transform Sine Cosine Graphs

Graphing Sine and Cosine With Different Coefficients (Amplitude and Period)
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)

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

Graphing Sine and Cosine with Phase (Horizontal) Shifts
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)

An Introduction to the Graphs of Sine and Cosine Functions

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