Calculate Cosine and Inverse Cosine
This free online calculator helps you compute cosine (cos) and inverse cosine (arccos) values with step-by-step explanations.
Calculator
Result:
Degrees (°)
Radians (rad)
Related Calculators
Cosine Values Table
| Angle (°) | Radians | Cos(θ) |
|---|---|---|
| 0° | 0 | 1.0 |
| 30° | π/6 | √3/2 ≈ 0.866 |
| 45° | π/4 | √2/2 ≈ 0.707 |
| 60° | π/3 | 0.5 |
| 90° | π/2 | 0 |
| 180° | π | -1 |
Interactive Cosine Graph
How It Works: A User Guide
- Select Mode: Use the dropdown menu to choose between "Cosine (cos)" and "Inverse Cosine (arccos)".
-
Enter Your Value: In the input box, enter the value you want to calculate.
- For Cosine mode, enter an angle (e.g., 90).
- For Inverse Cosine mode, enter a value between -1 and 1 (e.g., 0.5).
- Choose Units: For Cosine mode, select whether your input is in Degrees or Radians. For Inverse Cosine, the output will be shown in both.
- Calculate: Click the "Calculate" button. The results will appear below in both Degrees and Radians, along with a step-by-step explanation.
- Reset: Click "Reset" to clear all fields and start a new calculation.
Formulas
Cosine Function: The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle.
cos(θ) = Adjacent / Hypotenuse
Inverse Cosine (Arccosine): The inverse cosine of a ratio finds the angle whose cosine is that ratio.
arccos(x) = θ
Frequently Asked Questions (FAQs)
What is the range for Inverse Cosine?
The range of the inverse cosine function is typically from 0° to 180° or from 0 to π radians. This is why you should only enter values between -1 and 1.
What's the difference between cosine similarity and cosine distance?
Cosine similarity measures how similar two vectors are (their angle is close to 0°). Cosine distance measures their difference (1 - similarity).
How do I calculate cosine on a calculator?
Most calculators have a 'COS' button. You enter the angle value, and then press the 'COS' button to get the result. This tool simplifies that process for you.