> ## Documentation Index
> Fetch the complete documentation index at: https://docs.truemath.ai/llms.txt
> Use this file to discover all available pages before exploring further.

# Trigonometry

> Trigonometric, inverse, and hyperbolic functions, including how angle units are interpreted.

These functions take an angle and return a ratio, or take a ratio and return an angle. Each accepts a number or a [table](/math/types/tables), returning the same shape.

## Angle units

A bare number is interpreted as **degrees**. Attach an angle [unit](/math/units) to be explicit:

* `value` — degrees (the default)
* `value deg` — degrees
* `value rad` — radians

The inverse functions return their result in **degrees** by default; append `rad` to the call to get radians instead — for example, `asin(value rad)`.

## Sine, cosine, and tangent \[sin, cos, tan]

```
sin(value)
cos(value)
tan(value)
```

The sine, cosine, and tangent of an angle.

*Angles use the shared [angle units](#angle-units) — degrees unless you append `rad`.*

## Secant, cosecant, and cotangent \[sec, csc, cot]

```
sec(value)
csc(value)
cot(value)
```

The secant, cosecant, and cotangent of an angle — the reciprocals of cosine, sine, and tangent.

*Angles use the shared [angle units](#angle-units) — degrees unless you append `rad`.*

## Inverse functions \[asin, acos, atan]

```
asin(value)
acos(value)
atan(value)
```

The arc-sine, arc-cosine, and arc-tangent. `asin` and `acos` take a dimensionless ratio between -1 and 1; `atan` takes any dimensionless ratio. All three return an angle in degrees by default.

*Angles use the shared [angle units](#angle-units) — degrees unless you append `rad`.*

## Hyperbolic functions \[sinh, cosh, tanh, asinh, acosh, atanh]

```
sinh(value)
cosh(value)
tanh(value)

asinh(value)
acosh(value)
atanh(value)
```

The hyperbolic sine, cosine, and tangent, and their inverses.

<Note>
  Because angle units are unambiguous, `sin(45 deg)` and `sin((pi/4) rad)` refer to the same angle. See [Units](/math/units).
</Note>