Graphing Sine and Cosine

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline (equilibrium position) of the wave to its peak or trough. It determines the height of the wave.

Front

What is the period of a sine or cosine function?

Back

The period is the distance (or time) it takes for the function to complete one full cycle. For sine and cosine functions, the period is typically 2π.

Front

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

Back

Increasing the amplitude stretches the graph vertically, making the peaks and troughs higher and lower, respectively.

Front

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

Back

Changing the period compresses or stretches the graph horizontally, affecting how quickly the wave oscillates.

Front

What is the midline of a sine or cosine function?

Back

The midline is the horizontal line that runs through the center of the wave, equidistant from the maximum and minimum values.

Front

What is the phase shift in a sine or cosine function?

Back

The phase shift is the horizontal shift left or right for the graph of the function, determined by the value added or subtracted inside the function's argument.

Front

What is the general form of a sine function?

Back

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

Front

What is the general form of a cosine function?

Back

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

Front

What is the effect of a negative amplitude on the graph of a sine or cosine function?

Back

A negative amplitude reflects the graph across the midline, inverting the peaks and troughs.

Front

How do you determine the maximum and minimum values of a sine or cosine function?

Back

The maximum value is the amplitude added to the midline, and the minimum value is the midline subtracted from the amplitude.