The next question that comes up is if you have two sides of the right triangle, and you need to know the angle. The arc functions of sine, cosine and tangent resolve this issue. Let's use the same reference diagram for the following discussion.

The
arc sine function (`asin`

, also known as the
inverse sine) gives
theta (the angle in radians) from the height (AB) over the
hypotenuse (AC). The other arc functions, `acos`

,
and `atan`

,
behave as their more-familiar counterparts. So, the arc-cosine gives
theta from the base (BC) and the hypotenuse (AC); the arc-tangent,
from the height(AB) and the base (BC). Again, to convert
from radians to degrees, multiple the result by 180 / pi.

`asin` | [Generic] |

Returns the arc-sine of a real number

**Synopsis**

asin (x) => (y)

**Parameters**

xAn instance of `<real>`

.

**Return Values**

yAn instance of `<float>`

.

**Description**

Given the hypotenuse (AC) and the height (AB), the arc-sine gives theta in the diagram: the angle in radians.

`acos` | [Generic] |

Returns the arc-cosine of a real number

**Synopsis**

acos (x) => (y)

**Parameters**

xAn instance of `<real>`

.

**Return Values**

yAn instance of `<float>`

.

**Description**

Given the hypotenuse (AC) and the base (BC), the arc-cosine gives theta in Figure 12-2: the angle in radians.

`atan` | [Generic] |

Returns the arc-tangent of a real number

**Synopsis**

atan (x) => (y)

**Parameters**

xAn instance of `<real>`

.

**Return Values**

yAn instance of `<float>`

.

**Description**

Given the height (AB) over the base (BC), the arc-tangent gives theta in the diagram: the angle in radians.

`atan2` | [Generic] |

Returns the arc-tangent of a pair of real numbers

**Synopsis**

atan2 (y,x) => (z)

**Parameters**

yAn instance of `<real>`

.xAn instance of `<real>`

.

**Return Values**

zAn instance of `<float>`

.

**Description**

Given the height (AB) as

yand the base (BC) asx, the arc-tangent gives theta asz: the angle in radians.