Solve

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

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

1 year agoWe still doing these?

1 year agoI figured you'd have these mastered by now

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

1 year agoIDK, what work did you do to get that as the only answer?

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

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

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

1 year agoDoesn't that not fall within the unit circle tho

1 year agoOkay, then I guess you have your answer then.

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

1 year agoYeah that would just be 3pi/2

1 year agoCorrect

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

1 year agoAlso, 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.

1 year agomhm. going to get some sleep.

1 year agoits late for me and probably is for you too

1 year agoNo such thing as too late when you're a mil vet.

1 year agosleep is good though so be sure to get some. goodnight

1 year agoOf course. I always enjoy a good sleep.

1 year ago