Graphing Trigonometric Functions

Front

What is the amplitude of a trigonometric function?

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 the amplitude of the function y = 4cos(x)?

Back

The amplitude is the absolute value of the coefficient in front of the cosine function, which is 4.

Front

What is the maximum value of a sine function?

Back

The maximum value of a sine function is equal to the amplitude plus any vertical shift.

Front

What is the maximum value of the function y = -3sin(x) + 2?

Back

The maximum value is 2 + 3 = 5.

Front

What is the period of a trigonometric function?

Back

The period is the length of one complete cycle of the function.

Front

How do you calculate the period of the function y = cos(4x)?

Back

The period is calculated as 360 degrees divided by the coefficient of x, which is 4. Thus, the period is 90 degrees.

Front

Where does the graph of y=sin(x) begin its first cycle?

Back

The graph begins its first cycle at the point (0,0).

Front

What is the effect of a negative coefficient in front of a sine or cosine function?

Back

A negative coefficient reflects the graph across the x-axis.

Front

What is the amplitude of the function y = -5cos(x)?

Back

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

Front

What is a vertical shift in a trigonometric function?

Back

A vertical shift moves the graph up or down on the coordinate plane, determined by the constant added or subtracted from the function.