How to Use Inverse Tangent on Any Calculator

Finding the Hidden Button

The inverse tangent function (often written as tan⁻¹ or arctan) is a crucial tool for trigonometry, allowing you to convert a known ratio back into an angle.

However, unlike basic arithmetic operators, the inverse tangent button is rarely given its own dedicated key. Because it is the inverse operation of the standard tangent function, it usually “piggybacks” on the primary tan button as a secondary function.

In this comprehensive guide, we will walk you through exactly how to find and use this function across all major calculator brands and devices.

1. Physical Scientific & Graphing Calculators

If you’re in a classroom or engineering environment, you’re likely using a dedicated physical calculator. Here is how to navigate the most popular brands.

Texas Instruments (TI-84, TI-83, etc.)

Texas Instruments graphing calculators typically use a color-coded modifier key to access inverse functions.

1. Check Your Angle Mode: Press MODE. Ensure either Degree or Radian is highlighted depending on your needs. Press CLEAR to exit.
2. Press the 2ND key (usually yellow or blue, located in the top-left corner).
3. Press the TAN key.
4. Your screen will now display tan⁻¹(.
5. Type in your value (e.g., 1), close the parentheses ), and press ENTER.

Casio (fx-991EX ClassWiz, fx-82MS, etc.)

Casio calculators use a slightly different naming convention for their modifier key.

1. Press the SHIFT button (located at the top-left). (Note: On very old models, this might be labeled INV).
2. Press the tan button.
3. The display will show tan⁻¹.
4. Enter your ratio value.
5. Press the = key to calculate the angle.

2. Smartphone Native Calculators

You don’t need a dedicated device to calculate inverse tangent; the smartphone in your pocket is more than capable.

Apple iPhone (iOS)

The iPhone’s built-in calculator hides its scientific features to keep the interface clean.

1. Open the Calculator app.
2. Rotate your iPhone to landscape orientation. (Make sure Portrait Orientation Lock is turned off in your Control Center).
3. Tap the 2nd button (located near the middle-left) to toggle the inverse functions.
4. The tan button will instantly transform into tan⁻¹.
5. Type your number first, then tap the tan⁻¹ button to see the result.

Android (Google Calculator & Samsung)

Android devices also require a sideways glance or a swipe to reveal scientific functions.

1. Open your Calculator app.
2. Swipe left from the right edge, or rotate your phone sideways.
3. Tap the INV or Shift button (depending on your manufacturer).
4. Tap the tan⁻¹ or atan button.
5. Type your value and hit equals.

3. Desktop Software & Spreadsheets

For professionals doing bulk calculations, spreadsheet software is the best tool for the job.

Microsoft Excel and Google Sheets

Both Microsoft Excel and Google Sheets use identical syntax for trigonometric functions.

• Standard Arctan: Type =ATAN(value).
  • Note: This formula always returns the angle in radians.
• Convert to Degrees: To get a readable degree format, wrap it in a degrees formula: =DEGREES(ATAN(value))
• Two-Argument Arctan: If you are working with (x,y) coordinates and need the correct 360-degree quadrant, use =ATAN2(x_num, y_num).

Common Mistakes & Troubleshooting

If you are getting the wrong answer, 99% of the time it is due to Angle Mode Misconfiguration. Always check whether your calculator is looking for Degrees or Radians. For example, the inverse tangent of 1 is exactly 45 in Degree mode, but it is 0.78539 in Radian mode (π/4). Always double-check your settings!