Key Features of Sine & Cosine Graphs

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 maximum and minimum points. For example, if the maximum is 3 and the minimum is 1, the midline is at y=2.

Front

What is the period of a sine or cosine graph?

Back

Front

What is the amplitude of a sine or cosine graph?

Back

The amplitude is the height from the midline to the maximum (or minimum) point of the graph. It is calculated as half the distance between the maximum and minimum values.

Front

How do you determine the maximum value of a sine or cosine graph?

Back

The maximum value of a sine or cosine graph is equal to the amplitude plus the midline value. For example, if the amplitude is 3 and the midline is y=2, the maximum value is 5.

Front

How do you determine the minimum value of a sine or cosine graph?

Back

The minimum value of a sine or cosine graph is equal to the midline value minus the amplitude. For example, if the amplitude is 3 and the midline is y=2, the minimum value is -1.

Front

What is the phase shift in a sine or cosine graph?

Back

The phase shift is the horizontal shift left or right for the graph. It is determined by the value of 'c' in the function form y = a sin(b(x - c)) + d.

Front

What does the variable 'a' represent in the sine or cosine function?

Back

In the function y = a sin(bx) + d, 'a' represents the amplitude of the graph. It determines how tall the peaks and how deep the troughs are.

Front

What does the variable 'b' represent in the sine or cosine function?

Back

Front

What does the variable 'd' represent in the sine or cosine function?

Back

In the function y = a sin(bx) + d, 'd' represents the vertical shift of the graph. It moves the midline up or down.

Front

What is the relationship between sine and cosine graphs?

Back