arcsec

The trigonometric arcsecant function.

Syntax

• arcsec(x)

  • x is a real or complex number

Description

For real values, arcsec is the inverse of the restriction of the trigonometric secant function to [0, π] ∖ {0}; the domain is ℝ ∖ (−1, 1).

In general, arcsec(z) is defined as

arcsec(z) = π/2 + i⋅ln(i/z + √(1 − 1/z^2))

where z is a complex number. Notice that the general definition will be used also for real arguments in [−1, 1].

Examples

arcsec(2/√3)

0.523598775598	(=π/6)

arcsec(−1)

3.14159265359	(=π)

arcsec(0.5)

1.31695789692⋅i

arcsec(i)

1.57079632679 + 0.88137358702⋅i

See also

• sec