Sine & Cosine Graphs

Front

What is the period of the function y = A cos(Bx)?

Back

The period is given by the formula: Period = 2π/|B|.

Front

What does the parameter A represent in the function y = A sin[B(x-C)]+D?

Back

A represents the amplitude of the sine wave, which is the maximum distance from the midline.

Front

What does the parameter B affect in the function y = A sin[B(x-C)]+D?

Back

B affects the frequency of the wave, which is the number of cycles that occur in a unit interval.

Front

What does the parameter C represent in the function y = A sin[B(x-C)]+D?

Back

C represents the horizontal shift (phase shift) of the graph, moving it left or right.

Front

What does the parameter D represent in the function y = A sin[B(x-C)]+D?

Back

D represents the vertical shift of the graph, moving it up or down.

Front

How do you find the midline of a sine or cosine graph?

Back

The midline is found at y = D, where D is the vertical shift in the function.

Front

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

Back

The amplitude is 4, which is the coefficient of the sine function.

Front

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

Back

The amplitude is 3, as amplitude is always a positive value.

Front

What is the equation of the midline for the function y = 2 sin(x) - 1?

Back

The midline is y = -1.

Front

What is the frequency of the function y = 5 cos(2x)?

Back

The frequency is 2/2π, which simplifies to 1/π.