Sine and Cosine Graphs

Front

What is the period of the sine function y = sin(x)?

Back

The period of y = sin(x) is 2π.

Front

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

Back

The period of y = cos(x) is 2π.

Front

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

Back

The amplitude is 3.

Front

What is the amplitude of the function y = -2cos(x)?

Back

The amplitude is 2.

Front

How does the graph of y = -sin(x) differ from y = sin(x)?

Back

The graph of y = -sin(x) is a reflection of y = sin(x) across the x-axis.

Front

What is the effect of a coefficient greater than 1 in front of the sine function, such as in y = 4sin(x)?

Back

It stretches the graph vertically by a factor of 4.

Front

What is the effect of a coefficient less than 1 in front of the cosine function, such as in y = 0.5cos(x)?

Back

It compresses the graph vertically by a factor of 0.5.

Front

What is the phase shift of the function y = sin(x - π/2)?

Back

The phase shift is π/2 to the right.

Front

What is the phase shift of the function y = cos(x + π/3)?

Back

The phase shift is π/3 to the left.

Front

What is the period of the function y = 4cos(5x)?

Back

The period is 2π/5.