# Trigonometric Functions Calculator

URL: https://speedycalculator.com/calculators/math/trigonometry/
Last updated: 2026-10-25

> The trigonometry calculator gives sine, cosine, tangent, cosecant, secant and cotangent for any angle in degrees or radians, along with the reference angle.

## Inputs

- Angle (°, rad)

## Results

- sin
- cos
- tan
- csc
- sec
- cot
- Reference angle

## Formula

```
sin θ, cos θ, tan θ = sin θ ÷ cos θ
csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
```

## Explanation

Trigonometric functions relate angles to ratios of sides in right triangles and to points on the unit circle.

### How to use the Trigonometric Functions Calculator

- **Angle**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

The angle is converted to radians internally and each function is evaluated.

### What each result means

- **sin** = sin(rad([Angle]))
- **cos** = cos(rad([Angle]))
- **tan** = tan(rad([Angle]))
- **csc** = 1÷sin(rad([Angle]))
- **sec** = 1÷cos(rad([Angle]))
- **cot** = 1÷tan(rad([Angle]))

### Example values

How the main result changes when **Angle** changes and everything else stays at the example values above:

Angle (°)sin150.258822.50.3827300.537.50.6088450.7071600.866

## Worked example

Inputs — Angle: 30 °.

Results — **sin = 0.5**; cos = 0.8660254; tan = 0.57735027; csc = 2; sec = 1.15470054; cot = 1.73205081; Reference angle = 30 °.

## Key terms

- **Unit circle**: A circle of radius 1 used to define trig functions for all angles.

## FAQ

**Why is tan 90° undefined?**
cos 90° is zero, and division by zero is undefined.

**How do I remember the ratios?**
SOH-CAH-TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.

**What formula does the Trigonometric Functions Calculator use?**
sin θ, cos θ, tan θ = sin θ ÷ cos θ.