Graphing Sine and Cosine Functions

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to the peak (or trough). It is always a positive value.

Front

How do you determine the period of a sine or cosine function?

Back

The period is calculated as 2π divided by the coefficient of x in the function. For example, in y = sin(kx), the period is 2π/k.

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 horizontal 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 horizontal shift, and D is the vertical shift.

Front

What does a negative amplitude indicate in a sine or cosine function?

Back

A negative amplitude reflects the graph across the midline, but the amplitude itself is still considered positive.

Front

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

Back

Increasing the amplitude stretches the graph vertically, while decreasing it compresses the graph vertically.

Front

What is the effect of changing the period of a sine or cosine function?

Back

Changing the period affects the frequency of the wave; a shorter period results in more cycles in a given interval, while a longer period results in fewer cycles.

Front

What is the period of the function y = 3 cos(4x)?

Back

The period is 2π/4 = π/2.

Front

Write the equation of a cosine function with an amplitude of 3 and a period of 6π.

Back

y = 3 cos(1/2 x). (Since the period is 2π/B, B = 1/3.)

Front

What is the phase shift in the function y = sin(x - π)?

Back

The phase shift is π units to the right.