How to Put Tan Inverse in Mobile Calculator

The inverse tangent function (tan⁻¹) is a fundamental trigonometric calculation used in many fields including engineering, physics, and navigation. This guide explains how to perform this calculation on your mobile calculator with clear instructions and examples.

How to Calculate Tan Inverse

The inverse tangent function, often written as tan⁻¹(y/x) or arctan(y/x), calculates the angle whose tangent is the ratio of two values. This is particularly useful when you know the opposite and adjacent sides of a right triangle and need to find the angle.

Formula: tan⁻¹(y/x) = θ (where θ is the angle in degrees or radians)

The result is typically given in degrees or radians, depending on your calculator's mode. Most scientific calculators have a dedicated "tan⁻¹" button or an "inv" (inverse) function that you can use with the tangent button.

Step-by-Step Guide

For Android Devices

Open your calculator app (usually named "Calculator" or "Scientific Calculator").
If you're using the basic calculator, switch to scientific mode by tapping the "⋮" menu and selecting "Scientific Calculator".
Enter the value for y (opposite side) and press the multiplication button (×).
Enter the value for x (adjacent side) and press the division button (÷).
Press the "tan⁻¹" button (often labeled as "tan" with a small "-1" or "inv" button).
The result will appear in the display, showing the angle in degrees or radians.

For iOS Devices

Open the Calculator app from your home screen.
Tap the "⋮" menu and select "Scientific" if you're not already in scientific mode.
Enter the value for y (opposite side) and press the multiplication button (×).
Enter the value for x (adjacent side) and press the division button (÷).
Press the "tan⁻¹" button (often labeled as "tan" with a small "-1" or "inv" button).
The result will appear in the display, showing the angle in degrees or radians.

Note: If your calculator doesn't have a dedicated tan⁻¹ button, you can use the inverse function (often labeled "inv" or "2nd") in combination with the tangent button.

Common Mistakes

When calculating tan⁻¹ on a mobile calculator, several common errors can occur:

Incorrect order of operations: Entering the values in the wrong order (y/x instead of x/y) will give a different result.
Forgetting to change modes: If your calculator is in radians mode when you need degrees, or vice versa, the result will be incorrect.
Using the wrong function: Accidentally pressing tan instead of tan⁻¹ will give a completely different result.
Not clearing previous entries: If you don't clear the calculator before starting a new calculation, you might accidentally include old values.

Practical Examples

Let's look at a couple of practical examples to illustrate how to use tan⁻¹ in real-world scenarios.

Example 1: Finding an Angle in a Right Triangle

Suppose you have a right triangle with the opposite side measuring 3 units and the adjacent side measuring 4 units. To find the angle θ opposite the 3-unit side:

Enter 3 ÷ 4 on your calculator.
Press the tan⁻¹ button.
The result will be approximately 36.87 degrees.

Example 2: Calculating a Slope Angle

If you're measuring a slope where the vertical rise is 5 meters and the horizontal run is 12 meters, you can find the angle of elevation:

Enter 5 ÷ 12 on your calculator.
Press the tan⁻¹ button.
The result will be approximately 22.62 degrees.

FAQ

What is the difference between tan and tan⁻¹?

The tan function takes an angle and returns the ratio of the opposite side to the adjacent side of a right triangle. The tan⁻¹ function takes a ratio and returns the angle whose tangent is that ratio.

How do I change between degrees and radians on my calculator?

Most scientific calculators have a mode button that allows you to toggle between degrees and radians. Look for a button labeled "Deg" or "Rad" and press it to change modes.

What if my calculator doesn't have a tan⁻¹ button?

If your calculator doesn't have a dedicated tan⁻¹ button, you can use the inverse function (often labeled "inv" or "2nd") in combination with the tangent button. Press the inverse button first, then the tangent button.