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Mathematics 21 Online
Taco:

Solve

Taco:

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

Taco:

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

Hero:

We still doing these?

Hero:

I figured you'd have these mastered by now

Taco:

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

Hero:

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

Taco:

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

Hero:

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

Hero:

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

Taco:

Doesn't that not fall within the unit circle tho

Hero:

Okay, then I guess you have your answer then.

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

Taco:

Yeah that would just be 3pi/2

Hero:

Correct

Hero:

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

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.

Taco:

mhm. going to get some sleep.

Taco:

its late for me and probably is for you too

Hero:

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

Taco:

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

Hero:

Of course. I always enjoy a good sleep.

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