AngouriMath

Symbolics for .NET


Table of contents

AngouriMath

Navigation
Home Quick start Wiki Almanac Research What's new Try Use Angouri.org GitHub Report a bug Donate Contacts

← Back to list of members

TryRaiseToTheDoubledArgument​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​AngouriMath.​Entity)

 Method (no overloads)

Summary

expr, whose trigonometric functions are of theta and of 2 theta, rewritten in sin(2 theta) and cos(2 theta) alone
— or null where it is not even in theta.

Remarks

sin^2 = (1 - C)/2, cos^2 = (1 + C)/2 and sin cos = S/2, with
S and C the sine and cosine of the doubled argument; so a monomial
sin^p cos^q is a rational function of S and C exactly when
p + q is even, negative powers included, and an expression built from such
monomials by sums, products and quotients is one too. Going up to the doubled argument
where that holds gives polynomials of half the degree the other direction does:
sec(2t)/(1 + sec(t)^2 + 3 tan(t)) is answered in a third of a second written in
2t and declined after five written in t.

























Angouri © 2019-2023 · Project's repo · Site's repo · Octicons · Transparency · 4378 pages online