6.23.12 Transforming arctan into arccos: atan2acos
The atan2acos command transforms any atans in an
expression to acoss, using the identity
| arctan(x) = | | − arcsin | ⎛
⎜
⎜
⎜
⎜
⎝ | | ⎞
⎟
⎟
⎟
⎟
⎠ |
-
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:
| −arccos | ⎛
⎜
⎜
⎜
⎜
⎝ | | ⎞
⎟
⎟
⎟
⎟
⎠ |