# Trigonometry Calculator

Calculate sin, cos, tan, csc, sec, and cot for any angle in degrees or radians. Get all six trigonometric function values instantly. Free trig calculator.

## What this calculates

Evaluate all six trigonometric functions for any angle. Enter an angle in degrees or radians and instantly get the values of sine, cosine, tangent, cosecant, secant, and cotangent.

## Inputs

- **Angle** — The angle value to evaluate.
- **Angle Unit** — options: Degrees, Radians — Select whether the angle is in degrees or radians.

## Outputs

- **sin(θ)** — The sine of the angle.
- **cos(θ)** — The cosine of the angle.
- **tan(θ)** — formatted as text — The tangent of the angle. Undefined at 90° and 270°.
- **csc(θ)** — formatted as text — The cosecant (1/sin). Undefined when sin = 0.
- **sec(θ)** — formatted as text — The secant (1/cos). Undefined when cos = 0.
- **cot(θ)** — formatted as text — The cotangent (1/tan). Undefined when tan = 0.

## Details

Trigonometry is the branch of mathematics that studies relationships between the sides and angles of triangles. The six trigonometric functions are defined for any angle using the unit circle: sin(θ), cos(θ), tan(θ) = sin/cos, csc(θ) = 1/sin, sec(θ) = 1/cos, and cot(θ) = cos/sin.

For a right triangle with angle θ, sine is the ratio of the opposite side to the hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. The reciprocal functions (cosecant, secant, cotangent) are the reciprocals of these three primary functions.

Key identities include the Pythagorean identity sin²θ + cos²θ = 1, the double-angle formulas sin(2θ) = 2sin(θ)cos(θ) and cos(2θ) = cos²θ - sin²θ, and the sum formulas. Some values like tan(90°) and csc(0°) are undefined because they involve division by zero.

## Frequently Asked Questions

**Q: What are the six trigonometric functions?**

A: The six trig functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc = 1/sin), secant (sec = 1/cos), and cotangent (cot = 1/tan or cos/sin). They relate angles to ratios of sides in a right triangle or to coordinates on the unit circle.

**Q: When is tangent undefined?**

A: Tangent is undefined when cosine equals zero, which occurs at 90° (π/2) and 270° (3π/2), plus any full-rotation multiples. At these angles, the terminal side of the angle is vertical, so the ratio sin/cos involves division by zero.

**Q: How do I convert between degrees and radians?**

A: Multiply degrees by π/180 to get radians. Multiply radians by 180/π to get degrees. For example, 90° = π/2 radians, and π/3 radians = 60°.

**Q: What is the Pythagorean identity?**

A: The fundamental Pythagorean identity states that sin²(θ) + cos²(θ) = 1 for any angle θ. Dividing by cos² gives 1 + tan² = sec², and dividing by sin² gives cot² + 1 = csc².

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