Graphs of Sine & Cosine

Front

What is the equation of the graph for a cosine function with an amplitude of 5?

Back

y = 5 cos x

Front

What is the period of the sine and cosine functions?

Back

The period is 2π for the basic sine and cosine functions.

Front

What is the amplitude of a sine function represented as y = 3sin(x)?

Back

The amplitude is 3.

Front

What is the equation for a sine function with an amplitude of 2 and a vertical shift of 3?

Back

y = 2sin(x) + 3

Front

What is the amplitude of the function y = -2sin(x)?

Back

The amplitude is 2 (amplitude is always positive).

Front

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

Back

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

Front

What is the vertical shift in the function y = sin(x) + 4?

Back

The vertical shift is 4 units upward.

Front

What is the equation of a sine function with a period of 4π?

Back

y = sin(1/2 x) (since period = 2π/k, k = 1/2).

Front

How do you determine the amplitude of a cosine function?

Back

The amplitude is the absolute value of the coefficient in front of the cosine function.

Front

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

Back

The phase shift is π/2 units to the right.