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System Message

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

Guest (Customer)

[00:00:02] Find all solutions of the equation in the interval (0 , 2pi). Sec 4x = 2

[00:00:14] hey

Rohan M (Tutor)

[00:00:16] hi! how are you today?

[00:01:42] any ideas of where to begin?

[00:03:25] are you there?

Guest (Customer)

[00:05:04] yea

[00:05:11] i have no idea

[00:05:19] havent started it

Rohan M (Tutor)

[00:05:53] ok well are you familiar with the secant function?

Guest (Customer)

[00:07:09] yea its opposite of sec'

Rohan M (Tutor)

[00:07:35] ok, its also the inverse of cos

Guest (Customer)

[00:08:19] yea

Rohan M (Tutor)

[00:08:45] are you familiar with the unit circle?

Guest (Customer)

[00:09:18] a little, we touched on it in school

Rohan M (Tutor)

[00:09:51] ok great. basically its a tool to calculate sin and cos of common angles

Guest (Customer)

[00:10:05] ok

Rohan M (Tutor)

[00:10:39] also arcsin and arccos. so here, we can convert this equation to use cos instead of sec and then use the unit circle to find x

[00:11:11] can you convert this equuation to use cos?

Guest (Customer)

[00:12:04] (1/cos) 4x = 2

Rohan M (Tutor)

[00:12:39] ok, great

[00:13:13] now, we can take the inverse of both sides to cos out of the denominator

[00:13:16] can you do that?

Guest (Customer)

[00:14:04] I'm not really good at it

Rohan M (Tutor)

[00:14:39] ok, I can show you.
Basically all I'm doing is flipping both sides of the equation

[00:15:20] do you see what I did?

Guest (Customer)

[00:18:02] yea

Rohan M (Tutor)

[00:18:42] any idea what to do next?

Guest (Customer)

[00:23:09] divide by 4x

Rohan M (Tutor)

[00:23:25] the 4x is within the cos

[00:23:29] so you can't do that

[00:23:41] you have to take the inverse cos

Guest (Customer)

[00:24:03] Cos^-1

Rohan M (Tutor)

[00:24:11] thats right, good

[00:24:14] whats next?

Guest (Customer)

[00:25:16] divide by 4

Rohan M (Tutor)

[00:25:47] great, can you solve this?

Guest (Customer)

[00:26:30] yea

[00:27:16] 15

Rohan M (Tutor)

[00:27:22] ok, great. now remember the question asks for every solution between 0 and 2pi

[00:28:23] do you know how to find the other one?

Guest (Customer)

[00:28:45] not reallyType your message here.

Rohan M (Tutor)

[00:29:40] ok so if cos(4x) = 1/2 at the location i've marked then its also true ast this location

Guest (Customer)

[00:30:00] ok

Rohan M (Tutor)

[00:30:16] because cos is positive on the right side of the unit circle

[00:30:25] so this spot would be 360-15

Guest (Customer)

[00:31:02] 345

Rohan M (Tutor)

[00:31:16] thats right, good job!

[00:31:29] we're just out of time do you have any final questions?

Guest (Customer)

[00:32:07] no but can you clerify the answer for me please??

Rohan M (Tutor)

[00:32:55] sure. so you have 2 solutions.
15 degrees and 345 degrees

[00:33:10] x can be either of those 2 values to satisfy the equation?

[00:33:23] make sense?

Guest (Customer)

[00:33:28] yea

Rohan M (Tutor)

[00:33:48] great.
good luck with the rest of your work!