Question

Solve

Answer 1

\[\cot \theta \cos^2 \theta - 2 \cot \theta = 0\]
\[\cot \theta \cos^2 \theta - 2 \cot \theta = 0\]
\[\cot \theta (\cos^2 \theta -2) = 0\]

Answer 2

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

Angle values are just within the unit circle. No negatives

Answer 3

We still doing these?

Answer 4

I figured you'd have these mastered by now

Answer 5

\[\theta = \frac{ \pi }{ 2 }\]

is that the only angle

Answer 6

IDK, what work did you do to get that as the only answer?

Answer 7

\[\cot \theta = 0\]

There is
\[\cos^2 \theta = 2\] But that can't work

Answer 8

\(\cos \theta = \sqrt{2}\)


Basically find the angle

Answer 9

You always reduce down to either \(\sin\theta\) or \(\cos\theta\) with these kinds of problems then find the angle

Answer 10

Doesn't that not fall within the unit circle tho

Answer 11

Okay, then I guess you have your answer then.

Answer 12

But however, you should make sure that there is no other value besides the one you found for the other angle between 0 and 2pi

Answer 13

Yeah that would just be 3pi/2

Answer 14

Correct

Answer 15

Of course, when in doubt, you can just graph it: https://www.desmos.com/calculator/ziffjnwfkh

Answer 16

Also, next time you see \(\cos\theta = \sqrt{2}\) it would make sense that there is no solution for this since the range of cosine theta will always be -1< y < 1. And of course the square root of 2 is greater than one.

Answer 17

mhm. going to get some sleep.

Answer 18

its late for me and probably is for you too

Answer 19

No such thing as too late when you're a mil vet.

Answer 20

sleep is good though so be sure to get some. goodnight

Answer 21

Of course. I always enjoy a good sleep.