ARCSIN is the arcsine trigonometric function. ARCSIN is also called the inverse sine. The ARCSIN function accepts a number between -1 and 1 inclusive and returns the angle from the range -pi/2 through +pi/2 radians that has that sine.
ARCSIN is calculated by using a rational approximation for the argument x in the range 0 through 0.5 only. If x is outside this range, x is first reduced to being in the range in the following ways:
-
If x is less than 0, the following identity is used:
ARCSIN(x) = - ARCSIN(-x)
-
If x is greater than 0.86602, the following identity is used:
ARCSIN(x) = pi/2 - 2* ARCSIN(SQRT((1-x)/2))
-
If x is greater than 0.5 and less than 0.86602, the following identity is used:
ARCSIN(x) = pi/4 + 1/2* ARCSIN(2 * x**3 -1)
The value of pi/2 is listed under “Common Constants” later in this section.
