# Tutor.com Trigonometric Functions Session

##### Apr. 30, 2013

Session Transcript - Math - Trigonometry, 4/16/2013 9:25PM - Tutor.comSession Date: 4/16/2013 9:25PM
Length: 26.6 minute(s)
Subject: Math - Trigonometry

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

Guest (Customer)
[00:00:00] If sins= -3/7, xE [pi,3pi/2], find exact values for sin2x and cos2x.

Joanetta L (Tutor)
[00:00:17] Welcome to Tutor.com ! Let's get started.

Guest (Customer)
[00:00:27] hi

Joanetta L (Tutor)

Guest (Customer)
[00:01:20] hmm...

Joanetta L (Tutor)
[00:01:23] can you tell me what the xE indicates

Guest (Customer)
[00:01:31] it looks like this

Joanetta L (Tutor)
[00:01:54] oh, so sorry!!!
[00:02:08] It means x is an element of...

Guest (Customer)
[00:02:18] ohhh
[00:02:25] okay I see

Joanetta L (Tutor)
[00:02:41] so have you done a problem like this before?

Guest (Customer)
[00:03:05] I think so
[00:03:14] I don't think I remember now

Joanetta L (Tutor)
[00:03:20] k
[00:03:25] no problem
[00:03:36] we can get you started easily
[00:03:52] So the problem itself gives us a hint where to start
[00:04:08] It says that the sine value is negative
[00:04:28] and it tells us that the x value is in the what quadrant?

Guest (Customer)
[00:04:55] hmm
[00:05:11] the 3rd?

Joanetta L (Tutor)
[00:05:12] You got it!
[00:05:49] so i like to draw a triangle in the third quadrant to represent the info given to us
[00:06:21] that is draw a reference angle with a sine value of -3/7
[00:06:37] Does any of that sound familiar to you?

Guest (Customer)
[00:06:42] a little
[00:06:54] we never did any problems like this in class

Joanetta L (Tutor)
[00:07:16] ok, then I'll draw the triangle for you!!
[00:08:56] remember that sine is opposite over hypotenuse so that is what we have on our reference angle

Guest (Customer)
[00:09:23] oh yeah

Joanetta L (Tutor)
[00:09:29] good
[00:10:00] so if we are finding sin2x and cos2x, we are going to need the cosine value also
[00:10:18] Do you remember the formulas for these 2?

Guest (Customer)
[00:10:45] no we just learn this like.. today and some yesterday..

Joanetta L (Tutor)
[00:11:55] so that is the way we will calculate the exact value of sin2x
[00:12:00] k?

Guest (Customer)
[00:12:17] ok

Joanetta L (Tutor)
[00:12:49] so how can we find the cosine value if we know the sine for this triangle?

Guest (Customer)
[00:13:11] pythagorean ...?

Joanetta L (Tutor)
[00:13:13] You got it!
[00:13:51] so the horizontal will be what in this case?

Guest (Customer)
[00:14:11] sq rt 40?

Joanetta L (Tutor)
[00:14:13] You got it!
[00:14:40] so we should probably simplify that value
[00:15:07] would you like to write it on the board on the horizontal leg of the triangle?

Guest (Customer)
[00:15:46] ok

Joanetta L (Tutor)
[00:16:39] so can we simplify the sqrt of 40?

Guest (Customer)
[00:16:59] oh.. 2sq rt 10?

Joanetta L (Tutor)
[00:17:01] You got it!
[00:17:20] and is it + or - ?

Guest (Customer)
[00:17:30] -?

Joanetta L (Tutor)
[00:17:37] awesome!!
[00:17:44] Now we are ready to roll.
[00:18:16] so we need to sub in these values in the formula I wrote for you on the upper right corner
[00:18:23] can you do that?

Guest (Customer)
[00:18:39] ok
[00:19:24] is it 2(-3/7)(-40/7)?

Joanetta L (Tutor)
[00:19:52] the last ( ) needs editing

Guest (Customer)
[00:20:03] oh sq rt

Joanetta L (Tutor)
[00:20:18] yes, and -2sqrt 10

Guest (Customer)
[00:21:40] i have 12 sq rt 10/49

Joanetta L (Tutor)
[00:21:56] You got it!
[00:22:13] so now let's get the other one
[00:22:55] There are 3 different formulas for cos2x and in the interest of time, I have picked out the easiest one for this situation
[00:23:52] so this one only uses the sine value
[00:24:26] can you get that value for us?

Guest (Customer)
[00:24:51] is it.. 1-2(-3/7)(-3/7)?

Joanetta L (Tutor)
[00:25:03] yes it is!!

Guest (Customer)
[00:25:07] okay
[00:25:21] I have 31/49

Joanetta L (Tutor)
[00:25:23] You got it!
[00:25:35] very nice job!!
[00:25:51] Do you have any questions about what we did here tonight?

Guest (Customer)
[00:25:59] no

Joanetta L (Tutor)
[00:26:13] It's been a pleasure working with you
[00:26:18] Thanks for using Tutor.com.Â Please fill out the survey as you leave so we can learn how we can better help you in the future!Â

Guest (Customer)
[00:26:25] okay

Joanetta L (Tutor)
[00:26:32] thanks!!