Sine and Cosine Graphs

Front

What is the period of a sine or cosine function?

Back

The period is the distance along the x-axis for one complete cycle of the wave. For the standard sine and cosine functions, the period is 2π.

Tags

CCSS.HSF.TF.A.4

Front

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

Back

The period is π, calculated as 2π divided by the coefficient of x.

Tags

CCSS.HSF.TF.A.4

Front

What is the amplitude of a sine or cosine function?

Back

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

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

The amplitude is 3, which is the coefficient of the sine function.

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

The domain is all real numbers, expressed as (-∞, ∞).

Front

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

Back

The range is [-1, 1], meaning the output values of the cosine function are between -1 and 1.

Tags

CCSS.HSF-IF.C.7E

Front

What does the term 'midline' refer to in sine and cosine graphs?

Back

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

Tags

CCSS.HSF-IF.C.7E

Front

How does a phase shift affect the graph of a sine or cosine function?

Back

A phase shift moves the graph left or right along the x-axis, altering the starting point of the wave.

Tags

CCSS.HSF-IF.C.7E

Front

What is a vertical shift in the context of sine and cosine graphs?

Back

A vertical shift moves the entire graph up or down, changing the midline of the function.

Tags

CCSS.HSF-IF.C.7E

Front

What is the effect of a negative coefficient in front of a sine or cosine function?

Back

A negative coefficient reflects the graph across the x-axis.

Tags

CCSS.HSF-IF.C.7E