Taco:

Solve

5 months ago
Taco:

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

5 months ago
Taco:

\[0 \le \theta \le 2 \pi\] Angle values are just within the unit circle. No negatives

5 months ago
Hero:

We still doing these?

5 months ago
Hero:

I figured you'd have these mastered by now

5 months ago
Taco:

\[\theta = \frac{ \pi }{ 2 }\] is that the only angle

5 months ago
Hero:

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

5 months ago
Taco:

\[\cot \theta = 0\] There is \[\cos^2 \theta = 2\] But that can't work

5 months ago
Hero:

\(\cos \theta = \sqrt{2}\) Basically find the angle

5 months ago
Hero:

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

5 months ago
Taco:

Doesn't that not fall within the unit circle tho

5 months ago
Hero:

Okay, then I guess you have your answer then.

5 months ago
Hero:

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

5 months ago
Taco:

Yeah that would just be 3pi/2

5 months ago
Hero:

Correct

5 months ago
Hero:

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

5 months ago
Hero:

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.

5 months ago
Taco:

mhm. going to get some sleep.

5 months ago
Taco:

its late for me and probably is for you too

5 months ago
Hero:

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

5 months ago
Taco:

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

5 months ago
Hero:

Of course. I always enjoy a good sleep.

5 months ago