Graphing Sine and Cosine

Front

What is the period of a sine or cosine function?

Back

The period is the distance along the x-axis (horizontal) required for the function to complete one full cycle. For sine and cosine functions, the standard period is 2π.

Front

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

Back

The period can be determined using the formula: Period = 2π / |b|, where 'b' is the coefficient of x in the function y = a sin(bx) or y = a cos(bx).

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline (equilibrium position) of the wave to its peak (or trough). It is given by the absolute value of 'a' in the function y = a sin(bx) or y = a cos(bx).

Front

How does a change in amplitude affect the graph of a sine or cosine function?

Back

Increasing the amplitude stretches the graph vertically, making the peaks and troughs higher and lower, respectively. Decreasing the amplitude compresses the graph.

Front

What is the midline of a sine or cosine function?

Back

The midline is the horizontal line that runs through the middle of the wave, representing the average value of the function. It is determined by the vertical shift of the function.

Front

What effect does a horizontal shift have on the graph of a sine or cosine function?

Back

A horizontal shift (phase shift) moves the graph left or right along the x-axis. It is determined by the value of 'c' in the function y = a sin(b(x - c)) or y = a cos(b(x - c)).

Front

What is the vertical shift in a sine or cosine function?

Back

The vertical shift moves the graph up or down along the y-axis. It is determined by the value of 'd' in the function y = a sin(bx) + d or y = a cos(bx) + d.

Front

How do you graph a sine function?

Back

To graph a sine function, identify the amplitude, period, midline, and any shifts. Plot key points (0, π/2, π, 3π/2, 2π) and connect them smoothly.

Front

How do you graph a cosine function?

Back

To graph a cosine function, identify the amplitude, period, midline, and any shifts. Plot key points (0, π/2, π, 3π/2, 2π) starting from the maximum value and connect them smoothly.

Front

What is the relationship between sine and cosine functions?

Back

Sine and cosine functions are phase-shifted versions of each other. The sine function is a cosine function shifted to the right by π/2.