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 for one complete cycle of the wave. For the basic sine and cosine functions, the period is 2π.

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline (equilibrium position) to the peak (or trough) of the wave. For the basic sine and cosine functions, the amplitude is 1.

Front

How do you graph a sine function?

Back

To graph a sine function, start at the origin (0,0), plot points for key angles (0, π/2, π, 3π/2, 2π), and connect them smoothly to form a wave.

Front

How do you graph a cosine function?

Back

To graph a cosine function, start at the maximum point (0,1), plot points for key angles (0, π/2, π, 3π/2, 2π), and connect them smoothly to form a wave.

Front

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

Back

The phase shift is the horizontal shift left or right for the graph of the function. It is determined by the value of 'c' in the function y = a sin(b(x - c)) + d.

Front

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

Back

The vertical shift is the movement of the graph up or down, determined by the value of 'd' in the function y = a sin(bx) + d.

Front

What effect does changing the amplitude have on the graph?

Back

Changing the amplitude stretches or compresses the graph vertically. A larger amplitude results in taller peaks and deeper troughs.

Front

What effect does changing the period have on the graph?

Back

Changing the period stretches or compresses the graph horizontally. A smaller period results in more cycles within the same interval.

Front

What is the equation of a sine function with an amplitude of 3 and a period of π?

Back

The equation is y = 3 sin(2x). The factor of 2 in front of x gives a period of π.

Front

What is the equation of a cosine function with an amplitude of 2 and a phase shift of π/4?

Back

The equation is y = 2 cos(x - π/4). The term (x - π/4) indicates a phase shift to the right.