# Sine Calculator

Calculate the sine of any angle in degrees or radians. Find sin, arcsin, and cosecant values instantly. Free online sine function calculator.

## What this calculates

Calculate the sine of any angle in degrees or radians. Get the sin value, its inverse (arcsin), the cosecant, and related angle information all in one place.

## Inputs

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

## Outputs

- **sin(θ)** — The sine of the angle.
- **arcsin (degrees)** — The inverse sine of the result, in degrees (if |sin| ≤ 1).
- **csc(θ)** — formatted as text — The cosecant (1/sin). Undefined when sin = 0.
- **Related Angle Info** — formatted as text — The angle in the other unit and its quadrant.

## Details

The sine function is one of the fundamental trigonometric functions. For a right triangle, sin(θ) equals the ratio of the opposite side to the hypotenuse. On the unit circle, sin(θ) gives the y-coordinate of the point at angle θ.

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

The inverse sine function, arcsin(x) or sin⁻¹(x), returns the angle whose sine is x. It is defined for x in [-1, 1] and returns values in [-90°, 90°] (or [-π/2, π/2] radians). The cosecant, csc(θ) = 1/sin(θ), is the reciprocal of sine and is undefined when sin(θ) = 0.

## Frequently Asked Questions

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

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

**Q: What is arcsin (inverse sine)?**

A: Arcsin (also written sin⁻¹) is the inverse of the sine function. Given a value x between -1 and 1, arcsin(x) returns the angle θ such that sin(θ) = x. The result is always between -90° and 90°.

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

A: Sine equals zero at 0°, 180°, 360°, and every integer multiple of 180° (or π radians). At these angles, the terminal side lies along the x-axis, so the y-coordinate is 0.

**Q: What is the relationship between sine and cosine?**

A: Sine and cosine are complementary: sin(θ) = cos(90° - θ) and cos(θ) = sin(90° - θ). They also satisfy the Pythagorean identity: sin²(θ) + cos²(θ) = 1. Cosine leads sine by 90° in phase.

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