Cal11 calculator
Search calculator...

Cosine Calculator for Partial Degrees

Reviewed by Calculator Editorial Team

This cosine calculator computes the cosine of an angle in degrees, including partial degrees. Whether you're working with geometry, trigonometry, or physics, this tool provides precise results for angles with decimal places.

What is Cosine?

Cosine is a trigonometric function that relates the angle of a right triangle to the ratio of the length of the adjacent side to the hypotenuse. In other words, cosine answers the question: "What is the ratio of the adjacent side to the hypotenuse?"

For any angle θ in a right triangle, the cosine of θ is defined as:

cos(θ) = adjacent side / hypotenuse

In the unit circle, cosine corresponds to the x-coordinate of a point at angle θ from the origin.

How to Use the Calculator

Using the cosine calculator is straightforward:

  1. Enter the angle in degrees in the input field. You can use partial degrees (e.g., 45.5°).
  2. Click the "Calculate" button to compute the cosine value.
  3. View the result in the result panel below the calculator.
  4. Use the "Reset" button to clear the input and result.

The calculator handles angles from 0° to 360° and provides results with up to 10 decimal places.

The Formula

The cosine of an angle θ in degrees is calculated using the following formula:

cos(θ) = cos(θ × π / 180)

This formula converts the angle from degrees to radians before applying the cosine function, which is implemented in JavaScript's Math.cos() function.

Note: The calculator uses JavaScript's built-in Math.cos() function, which expects angles in radians. The conversion from degrees to radians is handled automatically.

Worked Examples

Example 1: 30°

To find cos(30°):

  1. Convert 30° to radians: 30 × π / 180 ≈ 0.5236 radians
  2. Compute cos(0.5236) ≈ 0.8660

The cosine of 30° is approximately 0.8660.

Example 2: 45.5°

To find cos(45.5°):

  1. Convert 45.5° to radians: 45.5 × π / 180 ≈ 0.7930 radians
  2. Compute cos(0.7930) ≈ 0.7055

The cosine of 45.5° is approximately 0.7055.

FAQ

What is the range of cosine values?
The cosine of any angle ranges from -1 to 1. For angles between 0° and 180°, cosine values are positive.
Can I use negative angles with this calculator?
Yes, the calculator accepts negative angles. For example, cos(-30°) is the same as cos(30°).
How precise are the results?
The calculator provides results with up to 10 decimal places, which is sufficient for most practical applications.