Graphing Sine and Cosine

Front

What is the graph of the sine function?

Back

The graph of the sine function is a smooth, continuous wave that oscillates between -1 and 1, with a period of 2π.

Tags

CCSS.HSF-IF.C.7E

Front

What is the graph of the cosine function?

Back

The graph of the cosine function is similar to the sine function, also oscillating between -1 and 1, but it starts at its maximum value of 1 when x=0.

Tags

CCSS.HSF-IF.C.7E

Front

What is the period of the sine function?

Back

The period of the sine function is 2π, meaning it repeats every 2π units along the x-axis.

Tags

CCSS.HSF.TF.A.4

Front

What is the period of the cosine function?

Back

The period of the cosine function is also 2π, indicating it repeats every 2π units along the x-axis.

Tags

CCSS.HSF.TF.A.4

Front

What is the amplitude of the sine function?

Back

The amplitude of the sine function is 1, which is the maximum distance from the midline (y=0) to the peak or trough.

Tags

CCSS.HSF-IF.C.7E

Front

What is the amplitude of the cosine function?

Back

The amplitude of the cosine function is also 1, representing the maximum distance from the midline (y=0) to the peak or trough.

Tags

CCSS.HSF-IF.C.7E

Front

How does a phase shift affect the sine function?

Back

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

Tags

CCSS.HSF-IF.C.7E

Front

How does a phase shift affect the cosine function?

Back

A phase shift moves the graph of the cosine function left or right along the x-axis, changing where the maximum value occurs.

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

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

Tags

CCSS.HSF-IF.C.7E

Front

What is the effect of changing the frequency of the sine function?

Back

Increasing the frequency of the sine function compresses the graph horizontally, resulting in more cycles within a given interval.

Tags

CCSS.HSF-IF.C.7E