Cosine is a fundamental trigonometric function. For a right triangle, cos(θ) = adjacent / hypotenuse. On the unit circle, it equals the x-coordinate of the point at angle θ.

What is the range of the cosine function?

Cosine always returns a value between -1 and 1 (inclusive). cos(0°) = 1, cos(90°) = 0, cos(180°) = -1, cos(270°) = 0, cos(360°) = 1.

How do I convert degrees to radians?

Multiply degrees by π/180. For example, 90° × (π/180) = π/2 ≈ 1.5708 radians. This calculator accepts both — just choose the right unit.

Why does cos(90°) show a very small number instead of exactly 0?

Floating-point arithmetic in computers cannot represent irrational multiples of π exactly, so cos(90°) may show something like 6.12e-17 instead of 0. The calculator rounds values within 1e-10 of 0 to display as 0.

Can I enter negative angles?

Yes. Negative angles rotate clockwise on the unit circle. cos(-θ) = cos(θ) because cosine is an even function.

What is the cosine of 45 degrees?

cos(45°) = √2/2 ≈ 0.7071. This is also equal to cos(π/4) in radians.

Cosine Calculator

Enter an angle in degrees or radians and instantly get its cosine value with a unit-circle visualization.

Enter Angle

Angle

Unit

Degrees (°) Radians (rad)

Common Angles

Unit Circle

The dot shows your angle; the x-coordinate equals cos(θ).

Step-by-Step Calculation

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Summary

The Cosine Calculator computes the cosine (cos) of any angle you enter, supporting both degrees and radians. It displays the result as a decimal, a fraction approximation when the value is a common exact value, and a live unit-circle diagram so you can see where your angle lands. Ideal for students, engineers, and anyone doing trigonometry work.

How it works

Enter an angle value in the input field.
Select whether the angle is in degrees or radians.
The cosine value is calculated instantly using the built-in Math.cos() function.
The unit-circle diagram updates to show the angle and the corresponding x-coordinate (cos value).
Copy the result or continue entering different angles.

Use cases

Verify trig homework answers without a physical calculator.
Quickly look up cosine values for common angles (0°, 30°, 45°, 60°, 90°).
Convert between degree and radian representations of an angle.
Check cosine values needed for physics or engineering formulas.
Visualize where an angle falls on the unit circle.
Compute cosine for large or negative angles with automatic normalization.

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu