Changes in Period and Phase Shift of Sine and Cosine Functions

What is the equation of the graph below? ans- y=cos(x+pi)

d

What is the period of y = sin(3x)

2pi/3

Which of the following is the graph of y = sin(0.5x)?

d

What is the phase shift of a periodic function?

a horizontal translation of the function

Which transformations are needed to change the parent cosine function to the cosine function below? ans- vertical stretch of 2, horizontal compression to a period of pi/2, phase shift of pi units to the right, vertical shift of 1 unit down

d

Which transformations are needed to change the parent cosine function to y=3cos(10(x-pi))?

vertical stretch of 3, horizontal compression to a period of pi/5, phase shift of p units to the right

Which of the following is the graph of y=cos(2(x+pi))?

d

Which term gives the horizontal length of one cycle of a periodic function?

period

The graph of y=cos(x+pi/2) is the graph of the y = cos(x) shifted in which direction?

pi/2 units to the left

Which term gives the number of cycles of a periodic function that occur in one horizontal unit?

frequency

What is the general equation of a cosine function with an amplitude of 3, a period of 4p, and a horizontal shift of -p?

c

Which of the following could be the equation of the function below? ans y=-2cos(2(x+pi))-1

c

Which transformations are needed to change the parent cosine function to ans- vertical compression of 0.35, horizontal compression to a period of pi/4, phase shift of pi/4 units to the right

c

What is the general equation of a sine function with an amplitude of 2, a period of pi, and a horizontal shift of p units?

a

The graph of y=sin(x-3pi/2) is the graph of the y = sin(x) shifted in which direction?

b 3pi/2 units to the right