Midline and Amplitude

Front

What is the midline of a sine function?

Back

The midline of a sine function is the horizontal line that runs through the middle of the maximum and minimum values of the function, representing the average value of the function.

Front

What is the amplitude of a sine function?

Back

The amplitude is the distance from the midline to the maximum or minimum value of the function. It is always a positive value.

Front

Back

The range is determined by the midline and amplitude. For this function, the midline is 2 and the amplitude is 4, so the range is [-2, 6].

Front

What is the effect of changing the amplitude in a sine function?

Back

Changing the amplitude affects the height of the peaks and the depth of the troughs of the graph, but does not affect the midline.

Front

What does a negative midline indicate in a sine function?

Back

A negative midline indicates that the entire graph of the sine function is shifted downward from the x-axis.

Front

What is the general form of a sine function?

Back

Front

What is the period of a sine function?

Back

Front

Back

The maximum value is found by adding the amplitude to the midline. Here, the maximum is 3 + (-1) = 2.

Front

What is the relationship between frequency and period in trigonometric functions?

Back

Front

Can the amplitude of a sine function be negative?

Back

No, the amplitude is always a non-negative value.