Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.


I set $\tan^{-1}(x)=\theta$, then I found the inverse, which is $\tan(\theta) = x$. That would mean that $\tan(\theta) = \frac{opp}{adj} = \frac{x}{1}$. What I need to do is find the hypotenuse. I know I have to use the Pythagorean theorem, but I don't have the hypotenuse, so it's not possible.

share|improve this question
If you have a right triangle, then the hypotenuse is $\sqrt{x^2+1}$. –  Sanath Mar 13 at 1:07
How did you get that? –  igknighton Mar 13 at 1:09
You have $opp.=x,adj.=1$. What do you get by Pythagoras' theorem? Also, the tag "calculus" is not appropriate - "trigonometry" would be better. –  Sanath Mar 13 at 1:10
Oh ok, I understand now –  igknighton Mar 13 at 1:14

1 Answer 1

up vote 1 down vote accepted

Since you know you have to use Pythagoras' theorem, by the converse of Pythagoras' theorem, the triangle must be a right triangle. Thus, since $opp.=x,adj.=1$, drawing out the triangle (if you need to), and using Pythagoras' theorem gives $$\boxed{Hypotenuse=\sqrt{x^2+1}}$$

share|improve this answer
I understand now. Thank you –  igknighton Mar 13 at 1:14

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.