Sine and Cosine Graphs

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough. For example, in the function y = 2sin(x), the amplitude is 2.

Front

What is the period of the sine and cosine functions?

Back

The period is the distance along the x-axis for one complete cycle of the wave. For y = sin(x) or y = cos(x), the period is 2π.

Front

What is the general form of a sine function?

Back

The general form is y = A sin(B(x - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.

Front

What is the general form of a cosine function?

Back

The general form is y = A cos(B(x - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.

Front

How does a vertical shift affect the sine and cosine graphs?

Back

A vertical shift moves the graph up or down. For example, in y = sin(x) + 2, the graph shifts up by 2 units.

Front

What does a negative amplitude indicate in a sine or cosine function?

Back

A negative amplitude reflects the graph across the x-axis. For example, y = -2sin(x) reflects the graph of y = 2sin(x) across the x-axis.

Front

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

Back

The value of B affects the period of the function. The period is calculated as 2π/|B|.

Front

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

Back

The value of C causes a horizontal shift. If C is positive, the graph shifts to the right; if negative, it shifts to the left.

Front

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

Back

The value of D causes a vertical shift. A positive D shifts the graph up, while a negative D shifts it down.

Front

What is the vertical shift for the function y = 4cos(0.5x + π) - 2?

Back

The vertical shift is down 2.