How to Convert to Degrees Tan Inverse in Windows Calculator

How to Use Windows Calculator for Inverse Tangent

Windows Calculator includes a scientific mode that allows you to calculate inverse trigonometric functions. Here's how to use it for inverse tangent in degrees:

1. Open the Calculator app from the Start menu.
2. Click the "Scientific" button in the top-left corner.
3. Enter the value for which you want to calculate the inverse tangent.
4. Click the "tan⁻¹" button (inverse tangent function).
5. The calculator will display the result in radians by default.
6. To convert the result to degrees, click the "Deg" button in the top-right corner.

For more precise calculations, you can use the formula method described in the next section.

Inverse Tangent Formula

The inverse tangent function (arctan) returns the angle whose tangent is the given number. The formula for converting radians to degrees is:

This formula converts the result from radians (which is what most calculators return by default) to degrees, which is often more useful for practical applications.

For example, if you have a right triangle with opposite side 3 and adjacent side 4, the tangent is 3/4 = 0.75. The inverse tangent in degrees would be:

Worked Examples

Let's look at two practical examples of calculating inverse tangent in degrees.

Example 1: Basic Triangle

Given a right triangle with opposite side 1 and adjacent side √3:

1. Calculate the tangent: tan = opposite/adjacent = 1/√3 ≈ 0.577
2. Calculate the inverse tangent in radians: arctan(0.577) ≈ 0.5236 radians
3. Convert to degrees: 0.5236 × (180/π) ≈ 30°

Example 2: Practical Application

You're measuring the angle of elevation to a point 50 meters away that's 15 meters higher than your position:

1. Calculate the tangent: tan = opposite/adjacent = 15/50 = 0.3
2. Calculate the inverse tangent in radians: arctan(0.3) ≈ 0.2915 radians
3. Convert to degrees: 0.2915 × (180/π) ≈ 16.74°

These examples show how inverse tangent calculations can be applied to real-world scenarios.