1. ## Trig ratios

Hi forum,

I've got a question - What is tan^-1(cot(x))? My calculator gives me a senseless answer.

Thanks.

2. ## Re: Trig ratios

Originally Posted by qwertyuiop
Hi forum,

I've got a question - What is tan^-1(cot(x))? My calculator gives me a senseless answer.

Thanks.
1. Go back to the basics. Use a right triangle (see attachment)

2. $\displaystyle \tan(A)=\frac ab~\implies~\tan^{-1}\left(\frac ab\right) = A$

3. $\displaystyle \angle(A)+\angle(B)=\frac \pi2$

4. $\displaystyle \cot(A)=\frac ba = \tan(B)$

5. ... and now you are able to determine $\displaystyle \tan^{-1}(\cot(A))$

3. ## Re: Trig ratios

Ok... I see... kinda...

x=tan^-1(cot(x))
x=tan^-2(tan(pi/2-x))
x=pi-x

Yes?

4. ## Re: Trig ratios

Originally Posted by qwertyuiop
... What is tan^-1(cot(x))?
Originally Posted by qwertyuiop
Ok... I see... kinda...

x=tan^-1(cot(x))
...
No.

That's completely different from your original question!

You only can state that

$\displaystyle \tan^{-1}\left(\cot(x) \right) = \frac \pi2 - x$

5. ## Re: Trig ratios

Sorry, that's what i meant

Thank you!