Algebraic Expression for cos(arctan(x)/3)
Date: 8/15/96 at 15:51:32 From: Anonymous Subject: Algebraic Expression for cos(arctan(x)/3) We know that cos(arctan(x)) equals 1/sqr(x^2+1). Likewise, cos(arctan(x)/2) can be written in an algebraic manner. The problem that I have been trying to solve for quite a while is to find an algebraic expression for cos(arctan(x)/3), in order to get rid of the trigonometric operands. Thanks in advance for trying to help me out. Arno de Puij, the Netherlands
Date: 10/29/96 at 15:3:59 From: Doctor Ceeks Subject: Re: Algebraic Expression for cos(arctan(x)/3) Hi, As far as I know, you will have to use the formula for the solutions to a cubic, which are algebraic, to get what you want. Using cos(x)= 4cos(x/3)^3 - 3cos(x/3), you can reduce cos(arctan(x)/3) by noting that cos(arctan(x))=1/root(x^2+1). Then you solve the cubic: 1/root(x^2+1) = 4y^3 - 3y for y. You can find the formula for the roots of a cubic equation at the site: http://mathforum.org/dr.math/problems/3degree.html -Doctor Ceeks, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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