Graphing Sine and Cosine

Front

What is the period of the sine and cosine functions?

Back

The period of the sine and cosine functions is 2π.

Front

Where does the graph of cosine begin?

Back

The graph of cosine begins at (0, 1).

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum value of the function from its midline. For example, in y = 2 sin x, the amplitude is 2.

Front

What is the equation of a cosine function with an amplitude of 5?

Back

The equation is y = 5 cos x.

Front

What is the equation of a sine function with an amplitude of 2?

Back

The equation is y = 2 sin x.

Front

How does changing the coefficient in front of sine or cosine affect the graph?

Back

Changing the coefficient affects the amplitude of the graph. For example, y = 3 sin x has an amplitude of 3.

Front

What is the effect of changing the frequency in the sine or cosine function?

Back

Changing the frequency affects the period of the graph. For example, y = sin(5x) has a period of 2π/5.

Front

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

Back

The phase shift is π/2 to the right.

Front

What is the vertical shift in the function y = sin x + 3?

Back

The vertical shift is 3 units up.

Front

What is the range of the sine and cosine functions?

Back

The range of sine and cosine functions is [-1, 1].