# sin#

ivy.sin(x, /, *, out=None)[source]#

Calculate an implementation-dependent approximation to the sine, having domain `(-infinity, +infinity)` and codomain `[-1, +1]`, for each element `x_i` of the input array `x`. Each element `x_i` is assumed to be expressed in radians.

Note

The sine is an entire function on the complex plane and has no branch cuts.

Special cases

For floating-point operands,

• If `x_i` is `NaN`, the result is `NaN`.

• If `x_i` is `+0`, the result is `+0`.

• If `x_i` is `-0`, the result is `-0`.

• If `x_i` is either `+infinity` or `-infinity`, the result is `NaN`.

For complex floating-point operands, special cases must be handled as if the operation is implemented as `-1j * sinh(x*1j)`.

Parameters:
• x (`Union`[`Array`, `NativeArray`]) – input array whose elements are each expressed in radians. Should have a floating-point data type.

• out (`Optional`[`Array`], default: `None`) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

`Array`

Returns:

ret – an array containing the sine of each element in `x`. The returned array must have a floating-point data type determined by type-promotion.

This function conforms to the Array API Standard. This docstring is an extension of the docstring in the standard.

Both the description and the type hints above assumes an array input for simplicity, but this function is nestable, and therefore also accepts `ivy.Container` instances in place of any of the arguments

Examples

With `ivy.Array` input:

```>>> x = ivy.array([0., 1., 2.])
>>> y = ivy.sin(x)
>>> print(y)
ivy.array([0., 0.841, 0.909])
```
```>>> x = ivy.array([0., 1.2, -2.3, 3.6])
>>> y = ivy.zeros(4)
>>> ivy.sin(x, out=y)
>>> print(y)
ivy.array([0., 0.932, -0.746, -0.443])
```
```>>> x = ivy.array([[1., 2., 3.], [-4., -5., -6.]])
>>> ivy.sin(x, out=x)
>>> print(x)
ivy.array([[0.841, 0.909, 0.141],
[0.757, 0.959, 0.279]])
```

With `ivy.Container` input:

```>>> x = ivy.Container(a=ivy.array([0., 1., 2., 3.]),
...                   b=ivy.array([-4., -5., -6., -7.]))
>>> y = ivy.sin(x)
>>> print(y)
{
a: ivy.array([0., 0.841, 0.909, 0.141]),
b: ivy.array([0.757, 0.959, 0.279, -0.657])
}
```
Array.sin(self, *, out=None)[source]#

ivy.Array instance method variant of ivy.sin. This method simply wraps the function, and so the docstring for ivy.sin also applies to this method with minimal changes.

Parameters:
• self (`Array`) – input array whose elements are each expressed in radians. Should have a floating-point data type.

• out (`Optional`[`Array`], default: `None`) – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

`Array`

Returns:

ret – an array containing the sine of each element in `self`. The returned array must have a floating-point data type determined by type-promotion.

Examples

```>>> x = ivy.array([0., 1., 2., 3.])
>>> y = x.sin()
>>> print(y)
ivy.array([0., 0.841, 0.909, 0.141])
```
Container.sin(self, *, key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False, out=None)[source]#

ivy.Container instance method variant of ivy.sin. This method simply wraps the function, and so the docstring for ivy.sin also applies to this method with minimal changes.

Parameters:
• self (`Container`) – input container whose elements are each expressed in radians. Should have a floating-point data type.

• key_chains (`Optional`[`Union`[`List`[`str`], `Dict`[`str`, `str`], `Container`]], default: `None`) – The key-chains to apply or not apply the method to. Default is `None`.

• to_apply (`Union`[`bool`, `Container`], default: `True`) – If True, the method will be applied to key_chains, otherwise key_chains will be skipped. Default is `True`.

• prune_unapplied (`Union`[`bool`, `Container`], default: `False`) – Whether to prune key_chains for which the function was not applied. Default is `False`.

• map_sequences (`Union`[`bool`, `Container`], default: `False`) – Whether to also map method to sequences (lists, tuples). Default is `False`.

• out (`Optional`[`Container`], default: `None`) – optional output container, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

`Container`

Returns:

ret – a container containing the sine of each element in `self`. The returned container must have a floating-point data type determined by type-promotion.

Examples

```>>> x = ivy.Container(a=ivy.array([1., 2., 3.]),
...                   b=ivy.array([-4., -5., -6.]))
>>> y = x.sin()
>>> print(y)
{
a: ivy.array([0.841, 0.909, 0.141]),
b: ivy.array([0.757, 0.959, 0.279])
}
```