# Tutor.com Trigonometric Functions Session

##### Jul. 15, 2012

Session Transcript - Math - Trigonometry, 5/30/2012 11:32PM - Tutor.comSession Date: 5/30/2012 11:32PM
Length: 17.8 minute(s)
Subject: Math - Trigonometry

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