Graphs of Sine & Cosine

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 its peak or trough. It is always a positive value.

Front

How do you determine the amplitude from the equation y = a sin(bx) + c or y = a cos(bx) + c?

Back

The amplitude is given by the absolute value of 'a'. For example, in y = 3 sin(2x), the amplitude is 3.

Front

What is the period of a sine or cosine function?

Back

Front

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

Back

Front

Write the equation for a sine function with an amplitude of 5 and a period of 2π.

Back

y = 5 sin(x) because the period is 2π when b = 1.

Front

What is the effect of changing the value of 'b' in the function y = a sin(bx)?

Back

Front

What is the midline of a sine or cosine function?

Back

The midline is the horizontal line that runs through the middle of the wave, represented by 'c' in the equations y = a sin(bx) + c or y = a cos(bx) + c.

Front

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

Back

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

Front

What is the equation of a cosine function with an amplitude of 4 and a vertical shift of -3?

Back

y = 4 cos(x) - 3.

Front

What is the amplitude of the function y = -2 cos(3x)?

Back

The amplitude is 2, as amplitude is always a positive value.