Arctan Calculator
Calculate the arctan of a given integer easily using our Arctan Calculator. To calculate the arcus tangent function in degrees or radians, use this online tool for arctangent calculations. Supports input of decimal numbers (0.5, 6, -1, etc.).
arctan() in degrees:
arctan() in radians:
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Table of Contents
What is an Arctan Calculator?
A mathematical instrument called an arctan calculator, often referred to as a tangent inverse calculator, uses this to find the angle whose tangent is a given number. Put more simply, it aids in determining the tangent function’s inverse function.
How to Use an Arctan Calculator
Input the Tangent Value: Enter the specific tangent value you want to find the inverse of.
Choose the Unit: Select the desired unit for the output angle. Common options include degrees, radians, and gradians.
Calculate: Click the “Calculate” or “Compute” button to obtain the corresponding angle.
About Arctan Function
On this page, we understand the arctan calculation. It is straightforward to comprehend. so let’s know it. Imagine you’re on a treasure hunt, and your secret map tells you to walk a certain distance on one side (let’s call it the “adjacent” side) and then turn a corner to reach buried loot (the “opposite” “side). The tangent function is like your compass here; it tells you how far you move toward the loot (opposite) compared to how far you move next to the corner (adjacent).
The arctan function, written as arctan(x) or tan⁻¹(x), is a compass’s best friend. It does the opposite! If you know the ratio of the sides you walked on (adjacent vs. opposite) and you use the arctan, this will tell you what angle you turned to reach the treasure.
using arctan example
Now here we understand the example of using arctan. To understand this, we have given the image of a right triangle below. In this image, we have given the lengths of two known sides.
The known side lengths are a = 20 and b = 12. A right triangle is shown at point C.
Now here we are: how can we find angle β at point B using the inverse tangent function? It is simple; here we will use the formula.
We all know the rules of trigonometry here. So we know the rule that the tangent of β is equal to the opposite side divided by the adjacent side.
So, tan(β) = b/aa = 12/20 = 0.6.
Now we will use the inverse function here. Using the inverse function, we will get degrees and radians.
So, β = arctan(0.6) = 30.96 ° (or 0.540 in radians).
Example : tan(β) = b / a = 15 / 26 = 0.577.
β = arctan(0.555) = 29.98 ° (or 0.523 in radians).
Frequently Asked Questions (FAQ)
1. What are the differences that exist between arctan and tan?
In arctan (or inverse tangent), the values representing the unknown angle of a right-angled triangle are determined when the value of the tangent is given as an input, while in tan, the ratio of the opposite side with the adjacent side of the right-angled triangle is determined from the input if the angle is given. In other words, tan gives the value, whereas arctan gives the value of an angle.
2. Is it possible to get an arctan value any larger than 90º?
No, arctan values will always be less than 90 degrees or 1800 or greater than -90 degrees or -1800 but will lie between 0 to 90 degrees or 0 to 1800 radians. If it is necessary to have an angle that is outside this range, then an additional 180° (or π radians depending upon the situation) can be added and removed.
3. What are the roles or real uses of arctan?
It has one application in navigation to determine the direction, civil engineering for civil structures angle, physics wave and motion problems, and computer graphics for rotation and orientation.
4. Is arctan the same as atan?
Yes, arctan and atan. Why both stand for arc tangent are the same. This is represented by either “arctan” or, more frequently, “atan” in use in programming languages and calculators.
5. How reliable is the arctan calculator?
The results obtained from an arctan calculator are as accurate as can be trusted to be precise, especially with the use of a digital tool as described above. The bulk of calculators round off the values as per the decimal places, and the results obtained within the floating-point representation are reasonable.
6. If I take the same input and don’t type it in using the degree button and instead use arctan, why do I get a different answer depending on the calculator I am using?
This is due to differences in the precision settings of calculators as well as the rounding modes applied to these appliances. Make sure that you are using a calculator that highlights how many decimal places are to be used for accuracy.
common arctan values table
| y | x = arctan(y) | |
|---|---|---|
| degrees | radians | |
| -∞ | -90° | -π/2 |
| -√3 | -60° | -π/3 |
| -1 | -45° | -π/4 |
| -1/√3 | -30° | -π/6 |
| 0 | 0° | 0 |
| 1/√3 | 30° | π/6 |
| 1 | 45° | π/4 |
| √3 | 60° | π/3 |
| +∞ | 90° | π/2 |
common arctangent values of fraction tangents
| x/y | arctan(x/y)degrees | arctan(x/y)radians |
|---|---|---|
| 1/2 | 26.565051° | 0.463648 rad |
| 1/3 | 18.434949° | 0.321751 rad |
| 3/4 | 36.869898° | 0.643501 rad |
| 4/3 | 53.130102° | 0.927295 rad |
| 1/6 | 9.462322° | 0.165149 rad |
To quickly get the cotangent of an angle given in degrees or radians, use our Cotangent Calculator. This free trigonometry calculator for cot(x) may be used to solve right triangles, circles, and other numbers.
To quickly get the tangent of an angle expressed in degrees or radians, use our tangent calculator. Right triangles, circles, and other figures involving right-angled triangles with a given angle x from which tan(x) can be calculated can be solved with the help of this trigonometry calculator.
The arccotangent of a given integer may be quickly calculated with the help of our Arccot Calculator. Allows for the entry of fractions (like 0.5, -0.5).