Definition
Arc tangent (arcctg or arccot) is the inverse trigonometric function.
Arccotangent x defined as the inverse function of the cotangent x.
If the cotangent of the angle у is х (ctg y = x), which means the arc tangent x equals y:
arcctg x = ctg-1 x = y
Note: ctg-1x means inverse cotangent, not cotangent to the power -1.
For example:
arctg 1 = ctg-1 1 = 45° = π/4 rad
The graph is arccotangent
The arc tangent function is written as y = arcctg (x). The graph in general looks like this:0 y < π, –∞ x + ∞):
Arc cotangent properties
Below, in tabular form, the main properties of the inverse tangent with formulas are presented.
| Property | Formula |
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«>Table of arc tangents
| 180° | π | -∞ | ||
| 150° | 5p/6 | 135° | 3p/4 | -1 |
| 120° | 2p/3 | 90 | Π / 2 | 0 |
| 60 | Π / 3 | 45 | Π / 4 | 1 |
| 30 | Π / 6 | 0 | 0 | ∞ |