Graphs of Sine & Cosine

Front

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

Back

The period is given by the formula 2π/k.

Front

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

Back

The period is given by the formula 2π/k.

Front

How do you determine the amplitude of a sine or cosine function?

Back

The amplitude is the absolute value of the coefficient in front of the sine or cosine function.

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(2x)?

Back

The amplitude is 2.

Front

What does it mean for a function to have a period of T?

Back

It means that the function repeats its values every T units along the x-axis.

Front

If the period of a sine function is 4π, what is the value of k in y = sin(kx)?

Back

k = 1/2.

Front

What is the effect of increasing the coefficient of x in y = sin(kx) on the period?

Back

Increasing k decreases the period of the function.

Front

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

Back

The amplitude affects the height of the peaks and the depth of the troughs of the graph.

Front

What is the period of the function y = 4sin(3x)?

Back

The period is 2π/3.