Arctan Calculator (Inverse Tangent)


Degrees:


Radians:

π radians:

The domain of x is all real numbers.

The range is -π/2 < y < π/2.

Graph of arctan (inverse tangent)

Use this calculator to determine the result of the inverse tangent of an entered value. The answer will be displayed in degrees, radians, and π radians. Only the range -π/2 < and < π/2 is considered.

Here’s more information on how to use the inverse tangent calculator. Additionally, you can explore the definition, graph, and important values of arc tangent.

How to use the inverse tangent calculator?

Step 1: Enter the value of x in the first input box. You can use any real value of x.

Step 2: The corresponding angle in degrees will be displayed on the right panel.

Step 3: The angle in radians and π radians will be displayed at the bottom.

Result in degrees, radians, and π radians

In a complete circle, we have a total of 360° or 2π radians. Therefore, 180° is equal to π radians. If we have an angle in degrees, and we want to convert it to radians, we have to divide it by 180 and multiply by π.

On the other hand, the difference between radians and π radians is that the result in “radians” already has the value of π included. The value of π is approximately 3.1415… For example, if we have 0.5 π radians, this is equal to 1.571.

What is the inverse tangent?

The inverse tangent, also known as the arc tangent, is the inverse function of the tangent. This means that the inverse tangent reverses the effect of the tangent function. For example, the tangent of 45° is equal to 1. Therefore, the inverse tangent of 1 is equal to 45°.

The inverse tangent function is denoted as tan-1(x) or also as arctan(x).

We can use the inverse tangent to find the angle if we know the ratios of the sides of a right triangle. For example, to find angle A in the triangle below, we can use arctan(x), where x equals a/b.

diagram-of-a-right-triangle-with-sides

What values of x can be used on the inverse tangent?

The inverse tangent accepts any real value of x as input. This is because the inverse tangent is the inverse function of the tangent. Therefore, their domains and ranges are swapped.

So since the tangent has a range that is equal to all real numbers, the domain of the inverse tangent is also equal to all real numbers.

Inverse tangent graph

The graph of the inverse tangent can be graphed considering that the values of x can be any real number and the values of y are located between -π/2 to π/2, with asymptotes at those points.

Graph of arctan (inverse tangent)

Inverse tangent domain

Using the graph of the inverse tangent, we can see that the values of x can be any value without any restrictions. Therefore, the domain of the inverse tangent is equal to all real numbers.

Inverse tangent range

From the graph of the inverse tangent, we can conclude that the output values of the function range from -π/2 to π/2, not including these values. Then, its range is -π/2 < y < π/2.

Table of the inverse tangent of common values

Value of xarctan(x)(rad)arctan(x)(°)
-∞-π/2-90°
-√3-π/3-60°
-1-π/4-45°
-1/√3-π/6-30°
00
1/√3π/630°
1π/445°
√3π/360°
π/290°

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