Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I recently started thinking about what inverse tangent is. It is obvious that the definition of tangent is $\frac{\sin x}{\cos x}$, however, what is inverse tangent?

I first thought $\tan^{-1} x = \frac{\sin^{-1} x}{\cos^{-1} x}$, but it didn't seem right when I graph it out.

One interesting I find is in most of the programming language I know, there are two atan functions. Does this mean there are two definition of $\tan^{-1}$?

share|cite|improve this question
up vote 3 down vote accepted

I will not comment on a relationship between arctan and arcsine and/or arccosine., other than I do not know of anything simple or commonly known.

In common programming languages, there are two arctan functions. $\phi=\text{atan}(y)$ is an angle whose tangent is $y$, such that $x \in (-\pi/2,\pi/2)$. This ignores anything in the second and third quadrant. To fix this, $\phi=\text{atan2}(x,y)$ (the arguments are sometimes reversed) is the angle whose cosine is $x$ and whose sine is $y$. This allows the second and third quadrant to be determined at the cost of having to input the sines and cosine instead of simply the tangent.

share|cite|improve this answer

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.