Transformations of Sine and Cosine Functions

Front

What is the amplitude of the function y = 3sin(7x) - 2?

Back

The amplitude is 3.

Front

In the equation y = \frac{1}{3}cos(\frac{1}{2}x + \frac{\pi}{3}), what is the phase shift?

Back

The phase shift is -\frac{2\pi}{3}.

Front

The phase shift is the same as...?

Back

The phase shift is the same as horizontal translation.

Front

What is the minimum value of the equation y = -5sin(\frac{1}{2}x + \pi) + 8?

Back

The minimum value is y = 3.

Front

Write an equation for the cosine function with amplitude = 3, period = 2\pi, phase shift: right \pi, vertical shift: up 5.

Back

y = 3cos(x - \pi) + 5.

Front

Define amplitude in the context of sine and cosine functions.

Back

Amplitude is the maximum distance from the midline of the graph to its peak or trough.

Front

What is the period of a sine or cosine function?

Back

The period is the distance along the x-axis for one complete cycle of the function.

Front

How do you find the period of the function y = a sin(bx)?

Back

The period is given by \frac{2\pi}{|b|}.

Front

What effect does a vertical shift have on the graph of a sine or cosine function?

Back

A vertical shift moves the graph up or down without changing its shape.

Front

What is a horizontal translation in the context of sine and cosine functions?

Back

A horizontal translation shifts the graph left or right along the x-axis.