# Tutor.com Functions Session

##### Apr. 22, 2013

Session Transcript - Math - Calculus, 3/28/2013 12:04AM - Tutor.comSession Date: 3/28/2013 12:04AM
Length: 9 minute(s)
Subject: Math - Calculus

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

Olivia (Customer)
[00:00:00] Explain the difference between cos^-1(x) and sec(x).

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[00:00:00] *** The student has 1180 minutes remaining. ***

Christina W (Tutor)
[00:00:05] Hello!
[00:00:09] Welcome to Tutor.com !

Olivia (Customer)
[00:00:10] Hi!

Christina W (Tutor)
[00:00:17] How are you this evening?

Olivia (Customer)
[00:00:40] Fine, though this problem is confusing me a little...

Christina W (Tutor)
[00:00:53] Ok let's see if I can help!
[00:01:04] so you are trying to differentiate between
[00:01:12] and
[00:01:25] what do you know about sec(x)?

Olivia (Customer)
[00:01:39] Yep!
[00:01:50] Well, it's 1 over cos(x) right?

Christina W (Tutor)
[00:01:54] right!
[00:02:13] ok and what do you know about cos^-1 (x)?

Olivia (Customer)
[00:02:30] It's the inverse of cos(x) right?

Christina W (Tutor)
[00:02:33] right!
[00:02:56] so the difference between these two is that cos^-1(x) is the inverse of cos
[00:03:07] but sec(x) is the reciprocal of cos(x)

Olivia (Customer)
[00:03:29] and the inverse is the negative reciprocal?

Christina W (Tutor)
[00:03:46] actually no, they are not very nicely related
[00:04:09] so the two are rather different

Olivia (Customer)
[00:04:52] Okay, so what's the difference between the reciprocal and the inverse?

Christina W (Tutor)
[00:05:07] so the reciprocal is when you just do 1/the function
[00:05:14] for example
[00:05:19] if we have f(x) = x^2
[00:05:26] the reciprocal is 1/x^2

Olivia (Customer)
[00:05:34] Okay.

Christina W (Tutor)
[00:05:41] but the inverse of x^2 is +/- sqrt(x)

Olivia (Customer)
[00:06:23] Oh, right, because to find the reciprocal you have to switch the x and y values and then solve for x.

Christina W (Tutor)
[00:06:34] that's to find the inverse
[00:06:41] reciprocal is just flipped over

Olivia (Customer)
[00:06:50] Right, I meant inverse!

Christina W (Tutor)
[00:07:08] that's ok!
[00:08:06] do you have any more questions about that?

Olivia (Customer)
[00:08:29] Nope, that should do it! Thanks for clearing that up!

Christina W (Tutor)
[00:08:37] you're welcoem!
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