Sin Cos Amp and Midline

Front

What is the period of a sine function?

Back

The period of a sine function is the length of one complete cycle before the function repeats. For the function y = sin(x), the period is 2π.

Front

What is the amplitude of a sine function?

Back

The amplitude of a sine function is the maximum distance from the midline to the peak (or trough) of the graph. It is the coefficient in front of the sine function.

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, representing the average value of the function. For y = a sin(bx) + c, the midline is y = c.

Front

What is the amplitude of y = 3sin(7x)?

Back

The amplitude is 3.

Front

What is the period of y = -3sin(x)?

Back

The period is 2π.

Front

How do you find the midline of y = 3cos(5x) - 2?

Back

The midline is y = -2.

Front

What does a negative amplitude indicate in a sine function?

Back

A negative amplitude indicates that the graph is reflected over the midline.

Front

If the function is y = 4cos(x), what is the amplitude?

Back

The amplitude is 4.

Front

What is the effect of changing the coefficient of x in y = sin(bx)?

Back

Changing the coefficient b affects the period of the function. The new period is given by 2π/b.

Front

What is the range of the function y = 2sin(x)?

Back

The range is from -2 to 2.