# Trigonometry

`acos`

¶

Syntax: `acos x`

(unary, atomic)

Returns the arccosine of `x`

; that is, the value whose cosine is `x`

. The result is in radians and lies between 0 and π. (The range is approximate due to rounding errors).

Null is returned if the argument is not between -1 and 1.

```
q)acos -0.4
1.982313
```

`asin`

¶

Syntax: `asin x`

(unary, atomic)

Returns the arcsine of `x`

; that is, the value whose sine is `x`

. The result is in radians and lies between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\). (The range is approximate due to rounding errors).

Null is returned if the argument is not between -1 and 1.

```
q)asin 0.8
0.9272952
```

`atan`

¶

Syntax: `atan x`

(unary, atomic)

Returns the arctangent of `x`

; that is, the value whose tangent is `x`

. The result is in radians and lies between \(-{\pi}{2}\) and \({\pi}{2}\). The range is approximate due to rounding errors.

```
q)atan 0.5
0.4636476
q)atan 42
1.546991
```

`cos`

¶

Syntax: `cos x`

(unary, atomic)

Returns the cosine of `x`

, taken to be in radians. The result is between `-1`

and `1`

, or null if the argument is null or infinity.

```
q)cos 0.2
0.9800666
q)min cos 10000?3.14159265
-1f
q)max cos 10000?3.14159265
1f
```

`sin`

¶

Syntax: `sin x`

Returns the sine of `x`

, taken to be in radians. The result is between `-1`

and `1`

, or null if the argument is null or infinity.

```
q)sin 0.5
0.4794255
q)sin 1%0
0n
```

`tan`

¶

Syntax: `tan x`

(unary, atomic)

Returns the tangent of `x`

, taken to be in radians. Integer arguments are promoted to floating point. Null is returned if the argument is null or infinity.

```
q)tan 0 0.5 1 1.5707963 2 0w
0 0.5463025 1.557408 3.732054e+07 -2.18504 0n
```