Finding Arc Sin

Date: 8/13/96 at 21:57:56
From: Anonymous
Subject: Using ArcTan, Sin, Cos, to Find Arc Sin

I am working on a computer program that requires Arc Sin and Arc Cos. 
My only problem is the software I am using does not have these 
functions. The following trig functions are supplied with the  
software: Sin, Cos, Tan, and Arc Tan. I would like to know if there is 
a way to create a formula to compute the Arc Sin, or Arc Cos using the 
available functions. An example of what I am looking for is something 
like the below example:

 arcsin 30 = .5

  ...... would the following work?

arcsine X
 arcsine:= arctan(X/Sqrt(1.0-(X^2)))

The only problem that I have run into is if the person calculating 
the arcsin of 1 or -1. The answer is not calculated correctly. I have 
been to several sites (through several books) and have had no luck 
finding the answer to my question.

Today everyone has either a calculator or a computer program to 
figure the answers for them. I would like to know a math formula, 
rather than entering it into a program or calculator. If there is any 
help you could provide, I would be greatful. 

Thanks for your time....

Date: 8/30/96 at 17:28:51
From: Doctor James
Subject: Re: Using ArcTan, Sin, Cos, to Find Arc Sin

You formula for Arcsine works great. Similarly, you can define
arccos:= arctan(sqrt(1.0-(x^2))/x). You are running into problems with 
1 and -1 (and 0 for arccos) because at those values the function is 
not defined. What you should do, then, is make it a function like...

function arcsine(X)
if x=1 then arcsine=pi/2
elseif x=-1 then arcsine=-pi/2
else arcsine=arctan(x/(sqrt(1-x^2)))

and similarly for arccos.

-Doctor James,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/