Algebra 2: Changes in Period and Phase Shift of Sine and Cosine Functions

When would two sine functions of the form y = sin(x - h) that have different values for h have the same graph? Explain.

-The period of the function is 2π,so every 2π the cycle will be again. -If the h-values differ by multiples of 2π,the function will have the same graph.

Which of the following have a frequency factor of b = 1?

-a sine function whose period is 2π radians -a cosine function with no phase shift whose x-coefficient is -1 -a sine function whose graph shows 2 cycles from -4π radians to 0 -a cosine function whose graph shows 1 cycle from 3π radians to 5π radians

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

2π/3

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

3π/2 units to the right

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

Frequency

What is the phase shift of a periodic function?

a horizontal translation of the function

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

b

What is the equation of the graph below?

d: y=cos(x+π)

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

period

Which transformations are needed to change the parent cosine function to y=0.35cos(8(x-π/4))?

vertical compression of 0.35, horizontal compression to a period of π/4, phase shift of π/4 units to the right

Which of the following could be the equation of the function below?

y=-2cos(2(x+π))-1

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

y=2sin(2(x-π))