# Trig ratios

• Nov 25th 2011, 11:30 PM
qwertyuiop
Trig ratios
Hi forum,

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

Thanks.
• Nov 25th 2011, 11:53 PM
earboth
Re: Trig ratios
Quote:

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

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

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

5. ... and now you are able to determine $\tan^{-1}(\cot(A))$
• Nov 26th 2011, 12:38 AM
qwertyuiop
Re: Trig ratios
Ok... I see... kinda...

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

Yes?
• Nov 26th 2011, 10:48 PM
earboth
Re: Trig ratios
Quote:

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

Quote:

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

$\tan^{-1}\left(\cot(x) \right) = \frac \pi2 - x$
• Nov 27th 2011, 12:42 AM
qwertyuiop
Re: Trig ratios
Sorry, that's what i meant :D

Thank you!