Inverse Tangent Calculator

The inverse tangent function is, as the name says, the inverse function of the trigonometric function tangent. An inverse function is, by definition, a function that takes as input the result of a function and returns the argument of the original function:

Inverting a function is not an easy task, and more often than not, there are no common rules to do so.

In the case of trigonometric functions, and in particular of the tangent function, the inverse functions take as argument a dimensionless number, and return an angle. If:

Then we define the inverse tangent function as:

The tangent is a periodic function, which repeats in the range with values between and . In the image below, you can see its graph:

We can invert a function by taking the reflection with respect to the diagonal of the first quadrant. However, due to the periodicity of the function, we would find something that is not exactly a function since for each value we would find infinite values. To properly define the inverse tangent function, we need to restrict the domain of the tangent function to the range . By doing so, we find a single chunk of the function, and we can define the inverse. Here is its graph:

You can clearly see that:

• The inverse tangent's domain is the entire -axis.
• The inverse tangent's range is restricted to .

Note also how the inverse tangent is not periodic anymore!

If you are reading this text, you probably asked yourself, "how to calculate the inverse tangent?". The answer is simple: use a calculator, as there is no easy way to find the values of this function using paper and pen.

inverse tangent calculator is the perfect tool for this purpose: insert a number in the valid domain of the inverse tangent (that is, the whole x-axis), and you'll get the result in no time. You can also use our inverse tangent calculator in reverse!

The inverse tangent function is known by many different names: we created a different tool for each of them! Try our:

• Arctan calculator;
• Arcus tangent calculator;
• Tan-1 calculator; and
• Tan inverse calculator!