Changes in Period and Phase Shift of Sine and Cosine Functions

Which is the graph of y = cos(x − π)?

1st option

Which is the graph of y = cos4(x − π)?

2nd option

This graph shows the function y = sin(x) shifted __ units to the __

30, left

Which is the graph of y = sin(0.25x) in degrees?

3rd option

Ok, you're welcome

:)

What is the vertical shift from the parent function?

0

This graph shows the function y = sin(x) shifted

B. y= sin(x+30)

Identify the values for the function y = cos 4(x - π) Amplitude= Period= Horizonal (phase) shift= __ units Vertical shift= __ units ___

1 pi/2 pi, 0, right

Which could be an equation for the graph?

y=cos(2x)

Drag the slider to change the value of b and observe the effect of b on the graph of the sine function. when b = 0.5 ,the period of orange graph is __ pi when b = 2 ,the period of orange graph is __ pi

4, 1

Which could be an equation for the graph?

B. y = -3cos(x)

Based on this evidence, When b > 1, the period __ When 0 < b < 1, the period __

decreases, increases

Identify the following using the graph Period: Frequency: Frequency factor:

pi 1/pi b=2

Drag the slider to change the value of h, and observe the effect of h on the graph of the cosine function. When h = π, the orange graph shifts __ units to the __ When h = −π, the orange graph shifts __ units to the __

pi, right pi, left

What happens when h = 2π or h = −2π? The orange graph __ the blue graph.

coincides with

Determine the following for the graph: Minimum: __ Maximum: __ What is the amplitude?

-3, 3, 3 (min, max, amp)