Category. Mathematics.
Abstract. Trigonometric arc secant: definition, plot, properties, identities and table of values for some arguments.
Reference. This article is a part of Librow scientific formula calculator project.
Arc secant is inverse of the secant function.
Arc secant is discontinuous function defined on entire real axis except the (−1, 1) range — so, its domain is (−∞, −1]∪[1, +∞). Function plot is depicted below — fig. 1.
[画像:Fig. 1. Plot of the arc secant function y = arcsec x.] Fig. 1. Plot of the arc secant function y = arcsecx.Function codomain is limited to the range [0, π/2)∪(π/2, π].
Complementary angle:
arcsecx + arccscx = π/2and as consequence:
arcsec csc φ = π/2 − φNegative argument:
arcsec(−x) = π − arcsecxReciprocal argument:
arsec(1/x) = arccosxSum and difference:
arcsecx + arcsecy = arcsec(xy /{1 − xy√[(1 − 1 /x2)(1 − 1 /y2)]})Some argument values:
| Argument x | Value arcsecx |
|---|---|
| 1 | 0 |
| √6 − √2 | π/12 |
| √(50 − 10√5) /5 | π/10 |
| √(2 − √2) | π/8 |
| 2√3 /3 | π/6 |
| √5 − 1 | π/5 |
| √2 | π/4 |
| √(50 + 10√5) /5 | 3π/10 |
| 2 | π/3 |
| √(4 + 2√2) | 3π/8 |
| √5 + 1 | 2π/5 |
| √6 + √2 | 5π/12 |
Trigonometric arc secant function arcsec of the real argument is supported by free version of the Librow calculator.
Trigonometric arc secant function arcsec of the complex argument is supported by professional version of the Librow calculator.
To calculate arc secant of the number:
arcsec(-1);To calculate arc secant of the current result:
arcsec(rslt);To calculate arc secant of the number x in memory:
arcsec(mem[x]);