Cosine Calculator

Calculate cosine values with detailed step-by-step solutions for angles in degrees or radians, including special angle recognition.

Enter Angle

Angle Value

Angle Unit

Degrees (°)Radians (rad)

• Common angles: 0°, 30°, 45°, 60°, 90°

• Cosine is maximum (1) at 0° and 360°

Result

Enter an angle to calculate its cosine value

Unit Circle & Cosine

On the unit circle, cosine represents the x-coordinate of the point where the angle intersects the circle.

cos(θ) = x-coordinate on unit circle

Special Angles

Degrees	Radians	Cosine (Exact)	Cosine (Decimal)
0°	0	1	1
30°	π/6	√3/2	0.8660
45°	π/4	√2/2	0.7071
60°	π/3	1/2	0.5
90°	π/2	0	0
180°	π	-1	-1
270°	3π/2	0	0
360°	2π	1	1

Cosine Function Properties

Domain & Range

Domain: All real numbers

Range: [-1, 1]

Periodicity

Period: 2π radians (360°)

cos(x + 2π) = cos(x)

Symmetry

Even function: cos(-x) = cos(x)

Symmetric about y-axis

Key Values

Maximum: 1 (at 0°, 360°, ...)

Minimum: -1 (at 180°, 540°, ...)

Important Cosine Identities

cos²(x) + sin²(x) = 1

Pythagorean Identity

cos(90° - x) = sin(x)

Cofunction Identity

cos(2x) = cos²(x) - sin²(x)

Double Angle Formula

cos(x + y) = cos(x)cos(y) - sin(x)sin(y)

Addition Formula

Frequently Asked Questions

The cosine function (cos) is a trigonometric function that relates an angle in a right triangle to the ratio of the adjacent side to the hypotenuse. On the unit circle, it represents the x-coordinate.

Tips

Enter the dimensions in the same unit for consistency.
Results update automatically as you type.
Use the unit selector to convert between different measurement systems.