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.

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.

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.

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.

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.

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.

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.

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.

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.

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.