Inverse trigonometric function
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(Redirected from Inverse tangent)
| name | usual notation | definition | range of x for real result | range of usual principal value |
|---|---|---|---|---|
| arcsine | y = arcsin(x) | x = sin(y) | -1 to +1 | -π/2 < y < π/2 |
| arccosine | y = arccos(x) | x = cos(y) | -1 to +1 | 0 < y < π |
| arctangent | y = arctan(x) | x = tan(y) | all | -π/2 < y < π/2 |
| arccosecant | y = arccsc(x) | x = cosec(y), y = arcsin(1/x) | -∞ to -1 and 1 to ∞ | -π/2 < y < 0 (or) 0 < y < π/2 |
| arcsecant | y = arcsec(x) | x = sec(y), y = arccos(1/x) | -∞ to -1 and 1 to ∞ | 0 < y < π/2 (or) π/2 < y < π |
| arccotangent | y = arccot(x) | x = cot(y), y = arctan(1/x) | all | -π/2 < y < 0 (or) 0 < y < π/2 |
The notations sin−1, cos−1, etc are often used for arcsin, arccos, etc, but this notation sometimes causes confusion between (e.g.) arcsin(x) and 1/sin(x).
In computer programming languages the functions arcsin, arccos, arctan, are usually called asin, acos, atan.
The inverse trigonometric function atan2(y,x) is available in many computer programming languages. It is defined as r = arctan(y/x), taking:-
if x = y = 0, then r = indefinite,
if x > 0 and y = 0, then r = 0,
if x < 0 and y = 0, then r = π, else
if y < 0, then -π < r < 0,
if y > 0, then 0 < r < π .
This function is used to find the direction from one point to another in 2-dimension Euclidean space.
For more information, see Trigonometric function#Inverse functions