Question

Solving for theta

Answer 1

\[\cot \theta \cos^2 \theta = 2 \cot \theta \]

@Vocaloid

Answer 2

@SmokeyBrown @zarkam21 any idea on the approach for this

Answer 3

Well, one thing you can do as a first step could be to divide both sides by cot(theta).
This leaves us with cos^2=2

Answer 4

From there, I think you'd take the square root of both sides, to get cos = sqrt(2).
Then you can do the inverse cosine to find the value of theta

Answer 5

wow you must be a genius SB

Answer 6

Nah, not at all

Answer 7

\[\cos ^{-1} = \sqrt2\]

Answer 8

?

Answer 9

for theta

Answer 10

Oh, sorry I was unclear. inverse cosine wouldn't be equal to sqrt(2). You would take the inverse cosine of sqrt(2) to find the value of theta.

Answer 11

\[\cos \theta = \sqrt 2\]
\[\theta = \cos ^{-1} (\sqrt2)\]

Does that fall in the unit circle?

Answer 12

yeah I misstyped that

Answer 13

It's supposed to fall between:

\[0 \le \theta \le 2 \pi\]

Answer 14

Oh, that's weird. Yeah, cosine can only go up to 1 on the unit circle, but sqrt(2) is greater than 1...

Answer 15

Undefined?

Answer 16

Cause you can't grab the arc cos of values outside of the domain, when working within the unit circle.

Answer 17

That makes sense. I guess the value would be undefined then.

Answer 18

Alright, ty

Answer 19

np