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 * **Aim: How do we sketch graphs of sine and cosine involving amplitude, period, and phase shift?**

During this lesson, you will graph sin and cos functions with phase shirts. Phase shifts are when the grpah either moves left or right, or it can move up or down, or a combination of left/right and up/down.

For the first video, you will how what causes a graph to shift either to the left or to the right. You should already know this rule from when we looked at graphing quadratic equations and tranformations of functions.

Here are some questions that you will be abl to answer watching the videos...


 * 1) What causes a graph to shift to the left?
 * 2) What causes a graph to shift to the right?
 * 3) How do we adjust the x-axis for a pahse shift?
 * 4) What is the equation to find a phase shift? Keep this with the information on amplitude and period.

[|Video 1]

[|Video 2]

For this set of videos you will look at a vertical phase shift, or up and down. There are three examples that are solved. Be sure to copy the notes and answer the questions below.

The standard form for any graph is y=asin(bx + c) + d.

1. if d is positive, in which direction does the graph move? 2. If d is negative, in which direction does the graph move?

[|Video 3]

[|Video 4]

[|Video 5]

Now try some for yourself...


 * y = 2sin(x - pi)
 * y=4cos(1/2 x + pi/2)
 * y=sin(x - pi/4)
 * y=2/3cos(x - pi/3)
 * y= - 1 + 1/2(cos 2x - 3pi)
 * y=1/4 sin (3/4x + pi/8) + 2

Can you go the other way??? If I give you a graph, can you give me the equation? Let's try a few

Directions: For numbers 3-14, write the equation of the sin or graphs. Watch out for periods, amplitudes and phase shifts.

[|Phase_shift_graphs.JPG]

Try this problem to receive ES with sin and cos graphing. This is optional. It will not hurt your grade if you attempt this and receive a NY.

[|Phase_Shift_ES.JPG]


 * Journal entry:** How is the periodic nature of the sin and cosine graphs affected by the coefficient of the function and/or the coefficient of the angle?