Enter an angle in degrees or radians and get the cosine (cos) value instantly. Choose your angle unit, type in your angle, and the calculator returns the cos result along with the equivalent angle in the other unit and a visual unit circle breakdown.
cos(x)
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Angle in Degrees
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Angle in Radians
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Angle in π Radians
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Cosine is one of the six fundamental trigonometric functions. For a right-angled triangle, it is defined as the ratio of the length of the adjacent side (base) to the hypotenuse. It is abbreviated as 'cos' and the formula is: cos(θ) = Adjacent / Hypotenuse.
The cosine function always returns a value between -1 and 1, inclusive. cos(0°) = 1, cos(90°) = 0, cos(180°) = -1, cos(270°) = 0, and cos(360°) = 1. Values outside this range are not possible for real angles.
To convert degrees to radians, multiply the degree value by π/180. For example, 60° × (π/180) = π/3 radians ≈ 1.0472 rad. You can use this calculator's angle unit selector to switch between degrees and radians automatically.
These are the most commonly used cosine values: cos(0°) = 1, cos(30°) = √3/2 ≈ 0.866, cos(45°) = √2/2 ≈ 0.707, cos(60°) = 0.5, and cos(90°) = 0. These values appear frequently in geometry, physics, and engineering problems.
The cosine function (cos) takes an angle as input and returns a ratio between -1 and 1. The inverse cosine (arccos or cos⁻¹) does the reverse — it takes a ratio between -1 and 1 and returns the corresponding angle. For example, cos(60°) = 0.5, and arccos(0.5) = 60°.
Cosine is positive in the 1st quadrant (0°–90°) and 4th quadrant (270°–360°), and negative in the 2nd quadrant (90°–180°) and 3rd quadrant (180°–270°). This follows from the unit circle definition where cosine represents the x-coordinate.
The law of cosines states that for a triangle with sides a, b, c and opposite angles α, β, γ: a² = b² + c² − 2bc·cos(α). It generalizes the Pythagorean theorem and is used to solve triangles when you know two sides and the included angle (SAS) or all three sides (SSS).
Yes. While the basic SOH-CAH-TOA definition applies to right triangles, cosine is defined for all angles via the unit circle and can be applied to any triangle using the law of cosines formula. This makes it applicable in navigation, physics, and engineering problems involving oblique triangles.