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System Message

[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).

System Message

[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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