Sine and Cosine Graphs

Front

What is the sine function?

Back

The sine function, denoted as sin(x), is a periodic function that describes the y-coordinate of a point on the unit circle as it rotates around the origin. It has a range of [-1, 1] and a period of 2π.

Front

What is the cosine function?

Back

The cosine function, denoted as cos(x), is a periodic function that describes the x-coordinate of a point on the unit circle as it rotates around the origin. It has a range of [-1, 1] and a period of 2π.

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 graph to its peak or trough. It is determined by the coefficient in front of the sine or cosine function.

Front

What is the period of a sine or cosine function?

Back

The period is the length of one complete cycle of the wave. For the functions y = sin(kx) or y = cos(kx), the period is given by 2π/k.

Front

How do you determine the amplitude of y = 3sin(x)?

Back

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

Front

How do you determine the period of y = 2cos(4x)?

Back

The period is 2π/4 = π/2.

Front

What is the phase shift of y = sin(x - π/2)?

Back

The phase shift is π/2 to the right.

Front

What is the vertical shift of y = cos(x) + 2?

Back

The vertical shift is 2 units upward.

Front

Write the equation for a cosine function with an amplitude of 5 and a period of π.

Back

y = 5cos(2x).

Front

What is the effect of changing the coefficient of x in y = sin(kx)?

Back

Changing the coefficient k affects the period of the sine function. The new period is 2π/k.