Writing Equations of Sine and Cosine

Front

What is the midline of a sine or cosine graph?

Back

The midline is the horizontal line that runs through the middle of the graph, representing the average value of the function.

Front

What is the general form of a sine function?

Back

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 midline.

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline to the peak (or trough) of the graph.

Front

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

Back

The period is calculated as 2π/B, where B is the coefficient of x in the function.

Front

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

Back

A negative amplitude reflects the graph across the midline.

Front

What is a phase shift in trigonometric functions?

Back

A phase shift is a horizontal shift left or right in the graph of the function.

Front

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

Back

The midline is y = -2.

Front

What is the period of the function y = 4cos(2x)?

Back

The period is π, calculated as 2π/2.

Front

What does the value of D represent in the function y = A sin(B(x - C)) + D?

Back

D represents the vertical shift or midline of the graph.

Front

What is the effect of changing the value of B in the function y = sin(Bx)?

Back

Changing B affects the period of the function; a larger B results in a shorter period.