# Tutor.com Complex Numbers Session

##### Apr. 21, 2012

Session Transcript - Math - Trigonometry, 4/15/2012 6:44PM - Tutor.comSession Date: 4/15/2012 6:44PM
Length: 25.6 minute(s)
Subject: Math - Trigonometry

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

Ariel (Customer)
[00:00:00] I need help with solving a problem

Eric K (Tutor)
[00:00:07] Welcome to Tutor.com ! I'm Eric.
[00:00:19] How may I help you today?

Ariel (Customer)
[00:00:36] convert each polar equation to a rectangular equation
[00:00:41] they only gave me r=10
[00:01:03] I dont know how to solve it since I think I'm missing what y is

Eric K (Tutor)
[00:01:23] I see! Let me give you a hint on this one.
[00:02:11] Using that formula on the right, how can you rewrite the r?
[00:02:46] Almost! Tell me it this is what you did:
[00:02:53] you took the square root of both sides right?
[00:03:24] The only thing is you can't simplify that anymore

Ariel (Customer)
[00:03:25] yes

Eric K (Tutor)
[00:04:19] Awesome! Now you have a formula for r
[00:04:49] You take it from here!

Ariel (Customer)
[00:05:24] but then what about finding the 0
[00:05:38] dont i use tan0=y/x?
[00:05:44] I dont even know what those value are

Eric K (Tutor)
[00:05:57] This one doesn't have an angle actually!
[00:06:03] Work it out and see what it comes out too
[00:06:21] it may look strangely familiar....
[00:06:36] so r is all you need for this one
[00:07:34] There you go! I want you to do one more step: square both sides
[00:08:45] Are you familiar with conic sections: circle, ellipses, etc.
[00:08:49] ?

Ariel (Customer)
[00:08:49] yes

Eric K (Tutor)
[00:08:56] What's that an equation of?

Ariel (Customer)
[00:09:22] a circle

Eric K (Tutor)
[00:09:32] Pretty neat huh?

Ariel (Customer)
[00:09:47] yes

Eric K (Tutor)
[00:09:49] let me show you something else too
[00:10:07] if you were to graph the equation r = 10
[00:10:21] there is no angle so the angle could be anything

Ariel (Customer)
[00:10:28] I see
[00:10:35] that makes sense

Eric K (Tutor)
[00:10:42] but r or the radius always has to be 10!
[00:10:48] Awesome!
[00:11:07] Is there anything else I could help you with or clear up?

Ariel (Customer)
[00:11:16] yeah
[00:11:25] I have a similar problem

Eric K (Tutor)
[00:11:38] Sure!

Ariel (Customer)
[00:12:00] am I suppose to mkae it y or x =?

Eric K (Tutor)
[00:12:27] You mean in the end like this:

Ariel (Customer)
[00:13:16] no

Eric K (Tutor)
[00:13:54] Oh I see...let's take a look
[00:14:43] Let's try a slightly different approach
[00:14:49] how could you rewrite sec?

Ariel (Customer)
[00:15:48] sec=1/cosx

Eric K (Tutor)
[00:15:52] Yes!
[00:16:15] Then do you see what you can do?

Ariel (Customer)
[00:16:32] no
[00:16:48] we dont know the angle measure

Eric K (Tutor)
[00:16:51] Hang on let's do one more step...
[00:16:57] multiply both sides by cos

Ariel (Customer)
[00:17:34] which makes x=6

Eric K (Tutor)
[00:17:38] There you go!
[00:18:42] The way you were doing it before would've have worked but one would simplify and the other would not. Is it okay if I show you really quickly?

Ariel (Customer)
[00:19:03] sure

Eric K (Tutor)
[00:20:00] so that one works out
[00:21:15] and the second one doesn't really simplify as well when you work it out
[00:21:59] So the other method works! Just takes a little longer!

Ariel (Customer)
[00:22:22] I see

Eric K (Tutor)
[00:22:26] and actually if you wanted too
[00:22:37] make the sin/cos into tan
[00:22:52] and then tan = y/x
[00:23:11] then divide both sides by y
[00:23:44] oh look! It does come out the same actually! A lot more work though.

Ariel (Customer)
[00:24:02] so there is more than one way to do this problem

Eric K (Tutor)
[00:24:19] Yep! Usually there are a bunch of ways to do these problems

Ariel (Customer)
[00:24:31] The first way was the shortest then?

Eric K (Tutor)
[00:24:34] as long as you get all into x's and y's you're good
[00:24:38] Yep!
[00:25:00] Is there anything I could clear up about what we did?

Ariel (Customer)
[00:25:05] no

Eric K (Tutor)
[00:25:23] Okay! It was good working with you!