Midline, Amplitude, and Period of Trig Functions

Front

What is the midline of a trigonometric function?

Back

The midline is a horizontal line that represents the average value of the function. It is the line that runs through the center of the wave, equidistant from the maximum and minimum values.

Front

How do you determine the amplitude of a trigonometric function?

Back

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

Front

What is the period of a trigonometric function?

Back

The period is the length of one complete cycle of the function. It is the distance along the x-axis after which the function repeats itself.

Front

What is the formula for the period of the sine function?

Back

Front

What is the formula for the period of the cosine function?

Back

Front

If a trigonometric function has a maximum value of 5 and a minimum value of -1, what is its amplitude?

Back

Front

If a trigonometric function has a midline at y=2, what are its maximum and minimum values if the amplitude is 3?

Back

The maximum value is 2 + 3 = 5, and the minimum value is 2 - 3 = -1.

Front

What does a midline of y=0 indicate about a trigonometric function?

Back

A midline of y=0 indicates that the function oscillates above and below the x-axis, with equal distance from the axis.

Front

How can you find the midline from a graph of a trigonometric function?

Back

Front

What is the effect of changing the amplitude on the graph of a trigonometric function?

Back

Changing the amplitude stretches or compresses the graph vertically. A larger amplitude results in taller peaks and deeper troughs.