Evaluate exactly: cot(arctan(-sqrt7)) I don't know where to begin

Question

zehanz · Answer

Begin with this: cot(x)=1/tan(x).
Your expression becomes:

1/tan(arctan(-sqrt(7)), so...

If you cannot solve it, please call again ;)

ZeHanz

anonymous · Answer

$$\frac{ 1 }{ \tan }(\tan(-\sqrt{7}))$$ Does that work? If it does, I still don't know where to go from there.

anonymous · Answer

Should I be using Pythagorean theorem? $$\tan(x) = -{\sqrt(7)} = -\frac{ {\sqrt(7)} }{ 1 } = \frac{ b }{ a }$$ $$\frac{ a }{ b } = \cot(x) = \frac{ 1 }{ -{\sqrt(7)} }$$This is the way i'm approaching it. Wrong? Right? Somewhere in between?

zehanz · Answer

tan(arctan(x)) = x, because tan and arctan are inverse functions: apply one of them to a number, put the result into the other and you have got your number back!
Therefore,
1/tan(arctan(-sqrt(7)) = 1/-sqrt(7).
If you are a purist, you can rewrite this the following way:

$$\frac{ 1 }{ -\sqrt{7} } = -\frac{ 1 }{ \sqrt{7} }=-\frac{ 1 }{ \sqrt{7} }*\frac{ \sqrt{7} }{ \sqrt{7} }=-\frac{ \sqrt{7} }{ 7 } = -\frac{ 1 }{ 7 }\sqrt{7}$$

Hope this helps!

ZeHanz

anonymous · Answer

It shows that I was going the right way, so It does help. Thanks for the help! I'm sure to have more as I go through this assignment and find that what I learned in class isn't so relevant to the work haha.