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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)

[00:00:00] graph funcion y=5/2 sin(x-2pi/3)
graph and plot all x-intercepts, minima and maxima within one period

Anthony B (Tutor)

[00:00:05] Welcome to Tutor.COM .
My name is Tony.

[00:00:09] I see you have a trigonometry question today.

[00:00:18] graphing a sine function.

[00:00:30] how far have you gone on this?

Guest (Customer)

[00:00:47] we just started this lesson
today

Anthony B (Tutor)

[00:01:22] OK, so you've just started this unit.

Guest (Customer)

[00:01:29] yes

Anthony B (Tutor)

[00:02:20] with these type of functions, there are actually 4 numbers (called parameters) that affect the graphing of the function, varying it

[00:02:30] from the parent sine function.

[00:02:51] it appears, though, that this function

[00:03:09] is only introducing 2 of these parameters:

[00:04:17] the first is the number 5/2 in your equation, which is usually assigned to a variable A:

[00:05:01] this parameter is associated with the amplitude

Guest (Customer)

[00:05:12] ok

Anthony B (Tutor)

[00:05:22] of the function, or how much the function varies vertically.

[00:05:33] now, the parent function, y
= sin x

[00:05:57] varies between the values -1 and 1; that is, its range is [-1,1]

[00:06:21] what this parameter, A, does is multiply that range

[00:06:53] so that it will be [-5/2, 5/2].

[00:07:26] so, instead of this:

[00:08:00] which is y = sinx

[00:08:17] we'll have this instead:

[00:09:01] do you follow how this parameter, 5/2, has

[00:09:14] multiplied the function values, essentially

[00:09:22] "stretching" the parent

[00:09:25] function vertically?

Guest (Customer)

[00:09:26] yes

Anthony B (Tutor)

[00:09:37] OK, good

[00:09:51] next, the number 2Ï€/3

[00:10:15] which appears subtracted from the independent variable x

[00:10:30] will have the effect of shifting the graph

[00:10:42] either left or right, depending on

[00:10:57] whether it's in the form

[00:11:06] x-C (shifts to the right)

[00:11:07] or

[00:11:15] x+C (shifts to the left)

[00:11:42] so, from the form we have here, will our graph

[00:11:50] be shifted to the right

[00:11:53] or the left?

Guest (Customer)

[00:11:57] right

Anthony B (Tutor)

[00:12:05] correct.

[00:12:13] by the way, this is called

[00:12:25] a "phase shift", if I haven't mentioned it earlier.

[00:12:34] so, what we can do

[00:12:46] is copy the blue graph, but shift it right

[00:12:52] 2Ï€/3 units, like:

[00:14:00] so that will give us this green graph, which

[00:14:21] now has the effects of the 5/2, giving us an enlarged

[00:14:31] range and amplitude;

[00:14:54] and the effect of the 2Ï€/3, which

[00:15:01] phase shifts our graph

[00:15:11] 2Ï€/3 units

[00:15:15] t the right.

[00:15:39] do you have

[00:15:45] any clarification questions

[00:15:54] about graphing sine waves, and the effects

[00:16:02] of parameters in changing those graphs?

Guest (Customer)

[00:16:09] so my minima is -5/2 and my
maxima 5/2?

Anthony B (Tutor)

[00:16:31] OK, very good

[00:16:39] those would be the modified

[00:16:45] min and maxs

[00:17:02] because of the A parameter.

Guest (Customer)

[00:17:06] oh ok

Anthony B (Tutor)

[00:17:12] any other clarification questions?

Guest (Customer)

[00:17:40] no i think i'm good thanks for
your help!