Phase Shifts

10.2

Phase Shift

Multiple Choice

Sine or Cosine?

• y=sin(x)

• y=cos(x)

Multiple Choice

Sine or Cosine?

• y=sin(x)

• y=cos(x)

Multiple Choice

The __________ represents half the distance between the max and min of a sine or cosine graph. 

• Period
• Frequency
• Extreme Values
• Amplitude

Multiple Choice

The period of a sine or cosine graph can be found by ....

• It's always 2π
• 2π/B
• B(2π)
• 2π+B

Multiple Choice

What is the period of either graph?  (y = sin(x) or cos x)

• $$\pi$$  

• $$2\pi$$  

• $$\frac{\pi}{2}$$  

• $$\frac{\pi}{4}$$  

Multiple Choice

What is the equation of graph? 

• y = sin 5x
• y =  cos 5x
• y = 5 sin x
• y = 5 cos x 

Multiple Choice

Find the amplitude of

$$y=-8\cos\left(\frac{7x}{4}\right)$$  .

• $$\frac{7}{4}$$  

• 8

• -8

• $$\frac{1}{8}$$  

Multiple Choice

Find a and d for the function f(x) = asin(x) + k such that the graph of f(x) matches the graph shown.

• a = 2, k = -1

• a = 2, k = 2

• a = 4, k = 1

• a = 4, k = -3

Multiple Choice

Determine the period of

$$y=3\cos\left(\frac{1}{6}x\right)-5$$  .

• $$\frac{\pi}{3}$$  

• $$\frac{1}{3}$$  

• $$6\pi$$  

• $$12\pi$$  

Open Ended

What are the [obvious] differences between the graphs of sine and cosine functions?

Multiple Choice

What is the equivalent way to rewrite the expression in standard form?

• $$y=\cos\left(\frac{1}{2}\left(x-\left(-\frac{\pi}{4}\right)\right)\right)$$  

• $$y=\cos\left(\frac{1}{2}x+2\pi\right)$$  

• $$y=\frac{1}{2}\cos\left(x+\frac{\pi}{4}\right)$$  

Fill in the Blank

EX. 1 What is the amplitude of the function?

Multiple Choice

EX. 1 What is the Period of the function?

• $$\pi$$  

• $$2\pi$$  

• $$4\pi$$  

• $$\frac{\pi}{4}$$  

Multiple Choice

EX. 1 What is the phase shift of the function?

• $$\frac{\pi}{4}\ Left$$  

• $$\frac{\pi}{4}\ Right$$  

• $$\frac{1}{2}\ Left$$  

• $$\frac{1}{2}\ Right$$  

Multiple Choice

EX. 1 What is the midline of the function?

• $$y=0$$

• $$y=\frac{1}{2}$$  

• $$y=x$$  

• $$y=4$$  

Multiple Choice

EX. 1 What is the phase shift of the function?

• $$\frac{\pi}{4}\ Left$$  

• $$\frac{\pi}{4}\ Right$$  

• $$\frac{1}{2}\ Left$$  

• $$\frac{1}{2}\ Right$$  

Multiple Choice

What is the equivalent way to rewrite the function?

• $$y=2\sin\left(2x+\pi\right)+1$$  

• $$y=-2\sin\left(2\left(x-\frac{\pi}{2}\right)\right)-1$$  

• $$y=\sin\left(-4x+\pi\right)+2$$  

Fill in the Blank

What is the amplitude of the function?

Multiple Choice

Since a=-2, what effect will it have in our graph?

• The peaks will be reflected.

• The graph will be below the x-axis

• It will shrink the graph

Multiple Choice

What is the period of the function?

• $$\pi$$  

• $$2\pi$$  

• 2

Multiple Choice

What is the midline of the function?

• $$y=0$$  

• $$y=-1$$  

• $$y=2x$$  

• $$y=-2$$  

Multiple Choice

What is the phase shift of the function?

• $$\frac{\pi}{2}\ Left$$  

• $$\frac{\pi}{2}\ Right$$  

• $$\pi\ Left$$  

• $$\pi\ Right$$  

Multiple Choice

What are both, the midline and amplitude of the graphed function?

• Midline: y=1

  Amp: 3

• Midline: y=0

  Amp: 3

• Midline: y=-2

  Amp: 4

• Midline: y=1

  Amp: 4