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/
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