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From: TMoore@massey.ac.nz (T. Moore)
Newsgroups: comp.lang.pascal
Subject: Re: Trigonometric function
Message-ID: <1123@massey.ac.nz>
Date: 1 Nov 90 22:55:02 GMT
References: <1650@marlin.NOSC.MIL>
Organization: Massey University, Palmerston North, New Zealand
Lines: 29
X-Reader: NETNEWS/PC Version 2.2


	I would like to use the "arccos" function---but it is
	not standard pascal.

	Is there a simple way to do this using standard pascal
	functions such as arctan,sin, or cos?

If cos(theta) = x then tan(theta) = sqrt(1-x*x)/x by simple trigonometry.

Therefore arccos(x) = arctan(sqrt(1-x*x)/x)
               if x > 0
(arccos(0) = pi/2)

I assume you want the principal value which is between 0 and pi.

(If x < 0 then the principal value of arctan is between -pi/2 and 0
 so you must add pi - I think: check with the manual).

If x is too close to zero you can find arctan(x/sqrt(1-x*x))
and add pi/2.

-- 

Terry Moore <T.Moore@massey.ac.nz>
 Department of Mathematics and Statisics,
 Massey University, Palmerston North, New Zealand

Kroneker:  "God made the natural numbers, the rest is the work of man."
Zermelo:   "But I can construct the natural from the empty set alone."
Bystander: "Who said 'You can't get something for nothing.'?"