# Transforming arctan into arccos: atan2acos

### 5.23.12 Transforming arctan into arccos: atan2acos

The atan2acos command transforms any atans in an expression to acoss, using the identity

arctan(x) =

π
2

− arcsin

⎛
⎜
⎜
⎜
⎜
⎝

x

√

1+x2

⎞
⎟
⎟
⎟
⎟
⎠

- atan2acos takes one argument:
  expr, an expression containing inverse trigonometric functions.
- atan2acos(expr) returns expr with any atans replaced by the appropriate acoss.

#### Example.

Input:

atan2acos(atan(x))

Output:

π
2

−arccos

⎛
⎜
⎜
⎜
⎜
⎝

x

√

1+x2

⎞
⎟
⎟
⎟
⎟
⎠