Key Features of Sinusoidal Functions

Front

What is the formula to find the period of a sinusoidal function?

Back

Front

What does the midline of a sinusoidal function represent?

Back

The midline is the horizontal line that runs through the middle of the wave, representing the average value of the function.

Front

How does a vertical shift affect the graph of a sinusoidal function?

Back

A vertical shift moves the graph up or down without changing its shape or period.

Front

What is the amplitude of a sinusoidal function?

Back

The amplitude is the maximum distance from the midline to the peak (or trough) of the wave.

Front

What is the general form of a sinusoidal function?

Back

y = A \sin(B(x - C)) + D or y = A \cos(B(x - C)) + D where A is amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

Front

How do you determine the maximum value of a sinusoidal function?

Back

The maximum value is found by adding the amplitude to the midline value.

Front

What is the effect of changing the value of B in the sinusoidal function?

Back

Front

What does a negative amplitude indicate in a sinusoidal function?

Back

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

Front

How do you find the equation of the midline from a sinusoidal graph?

Back

The midline is the average of the maximum and minimum values of the function.

Front

What is the phase shift in a sinusoidal function?

Back

The phase shift is the horizontal shift left or right for the graph, determined by the value of C in the function.