# Cosine Calculator

Calculate the cosine of any angle in degrees or radians. Find cos, arccos, and secant values instantly. Free online cosine function calculator.

## What this calculates

Calculate the cosine of any angle in degrees or radians. Get the cos value, its inverse (arccos), the secant, and related angle information.

## Inputs

- **Angle** — The angle to evaluate.
- **Angle Unit** — options: Degrees, Radians — Select degrees or radians.

## Outputs

- **cos(θ)** — The cosine of the angle.
- **arccos (degrees)** — The inverse cosine of the result, in degrees.
- **sec(θ)** — formatted as text — The secant (1/cos). Undefined when cos = 0.
- **Related Angle Info** — formatted as text — The angle in the other unit and its quadrant.

## Details

The cosine function is a fundamental trigonometric function. For a right triangle, cos(θ) equals the ratio of the adjacent side to the hypotenuse. On the unit circle, cos(θ) gives the x-coordinate of the point at angle θ.

The cosine function has a range of [-1, 1] and a period of 360° (2π radians). Key values include cos(0°) = 1, cos(30°) = √3/2 ≈ 0.8660, cos(45°) = √2/2 ≈ 0.7071, cos(60°) = 0.5, and cos(90°) = 0. Cosine is positive in Quadrants I and IV, and negative in Quadrants II and III.

The inverse cosine function, arccos(x) or cos⁻¹(x), returns the angle whose cosine is x. It is defined for x in [-1, 1] and returns values in [0°, 180°] (or [0, π] radians). The secant, sec(θ) = 1/cos(θ), is the reciprocal of cosine and is undefined when cos(θ) = 0 (at 90° and 270°).

## Frequently Asked Questions

**Q: What is the cosine function?**

A: Cosine is a trigonometric function that gives the ratio of the adjacent side to the hypotenuse in a right triangle. On the unit circle, cos(θ) is the x-coordinate at angle θ. Its values range from -1 to 1.

**Q: What is arccos (inverse cosine)?**

A: Arccos (also written cos⁻¹) is the inverse of the cosine function. Given a value x between -1 and 1, arccos(x) returns the angle θ such that cos(θ) = x. The result is always between 0° and 180°.

**Q: When is cosine equal to zero?**

A: Cosine equals zero at 90°, 270°, and every odd multiple of 90° (i.e., 90° + 180°n). At these angles, the terminal side lies along the y-axis, so the x-coordinate is 0.

**Q: How is cosine related to the dot product?**

A: The dot product of two vectors A and B equals |A| |B| cos(θ), where θ is the angle between them. This means cos(θ) = (A · B) / (|A| |B|). Cosine thus measures the directional similarity between two vectors.

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Source: https://vastcalc.com/calculators/math/cosine
Category: Math
Last updated: 2026-04-21