Sine and Cosine Graph

Front

What is the amplitude of a sine or cosine graph?

Back

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

Front

How do you determine if a function is sine or cosine based on its graph?

Back

A sine graph starts at the midline (0) and goes up, while a cosine graph starts at its maximum value.

Front

What is the period of a sine or cosine function?

Back

Front

What is the formula for the amplitude of a sine or cosine function?

Back

The amplitude is given by the coefficient in front of the sine or cosine function, represented as |A| in the function y = A sin(Bx + C) + D.

Front

Back

Front

How does a vertical shift affect the sine or cosine graph?

Back

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

Front

What is the effect of changing the coefficient of x in the function y = sin(Bx)?

Back

Front

What is the midline of a sine or cosine graph?

Back

The midline is the horizontal line that runs through the middle of the graph, representing the average value of the function.

Front

How do you find the maximum and minimum values of a sine or cosine function?

Back

The maximum value is the amplitude plus the vertical shift, and the minimum value is the negative amplitude plus the vertical shift.

Front

What is the relationship between the amplitude and the height of the peaks in a sine or cosine graph?

Back

The height of the peaks is equal to the amplitude when measured from the midline.