Key Features of Sine and Cosine

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. It is calculated as the absolute value of the coefficient in front of the sine or cosine function.

Front

How does a horizontal shift affect the graph of a sine or cosine function?

Back

A horizontal shift moves the graph left or right along the x-axis. It is determined by the value added or subtracted inside the function's argument.

Front

What is the period of a sine or cosine function?

Back

Front

What does a negative amplitude indicate in a cosine function?

Back

A negative amplitude reflects the graph across the midline, effectively flipping it upside down.

Front

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

Back

The vertical shift is determined by the constant added or subtracted outside the sine or cosine function. It moves the graph up or down.

Front

What is the effect of changing the coefficient of x in the argument of sine or cosine?

Back

Changing the coefficient of x (the 'b' value) affects the period of the function. A larger 'b' value results in a shorter period.

Front

Back

The amplitude is 5, which is the absolute value of -5.

Front

Back

Front

Back

The graph is shifted up by 3 units.

Front

Back

The maximum value is found by adding the amplitude to the vertical shift: 2 + (-1) = 1.