Sine and Cosine - Amplitude and Period

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline (equilibrium position) of the graph to its peak or trough. It is always a positive value.

Front

How do you determine the amplitude from the function y = A sin(Bx) or y = A cos(Bx)?

Back

The amplitude is given by the absolute value of A. For example, in y = -4 sin(3x), the amplitude is | -4 | = 4.

Front

What is the period of a sine or cosine function?

Back

Front

How do you find the period from the function y = A sin(Bx) or y = A cos(Bx)?

Back

Front

What is the effect of changing the amplitude on the graph of a sine or cosine function?

Back

Changing the amplitude stretches or compresses the graph vertically. A larger amplitude results in taller peaks and deeper troughs.

Front

What happens to the graph of a sine or cosine function when the period is altered?

Back

Altering the period stretches or compresses the graph horizontally. A shorter period results in more cycles within the same interval.

Front

If y = 2 sin(3x), what is the amplitude and period?

Back

Front

If y = -5 cos(2x), what is the amplitude and period?

Back

Front

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

Back

The amplitude is 7.

Front

What is the period of the function y = 4 cos(4x)?

Back