arcsin

The trigonometric arcsine function.

Syntax

• arcsin(x)

  • x is a real or complex number

Description

For real values, arcsin is the inverse of the restriction of the trigonometric sine function to [−π/2, π/2]; the domain is [−1, 1].

In general, arcsin(z) is defined as

arcsin(z) = −i⋅ln(i⋅z + √(1 − z^2))

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

Examples

arcsin(√3/2)

1.0471975512	(=π/3)

arcsin(−1/2)

−0.523598775598	(=−π/6)

arcsin(2)

1.57079632679 − 1.31695789692⋅i

arcsin(i)

0.88137358702⋅i

See also

• sin