For example, what is $\sin(2x) = 2 \sin x \cos x$ called? Here are a few names I can think of:

  • Double angle formula for sin
  • Double angle formula of sin
  • Sin double angle formula
  • Double angle sin formula

However, none of these sound "right." Do they have proper names?

  • 1
    $\begingroup$ I've learned it under the name double angle formula, but I doubt if there is a proper name for them $\endgroup$ – user160738 Dec 6 '16 at 23:29
  • $\begingroup$ I call them the special cases of the Chebyshev polynomials. Particularly the second kind for $\sin$, first kind for $\cos$. $\endgroup$ – Simply Beautiful Art Dec 6 '16 at 23:30
  • $\begingroup$ @SimpleArt Chebyshev polynomials are polynomials though, correct? These are equations so not even functions like the Chebyshev polynomials $\endgroup$ – Will Fisher Dec 6 '16 at 23:40
  • $\begingroup$ @WillFisher Here we have $n=2$.$$\sin(x)U_{n-1}(\cos(x))=\sin(nx)$$ $\endgroup$ – Simply Beautiful Art Dec 6 '16 at 23:43
  • $\begingroup$ @WillFisher Oh, I see your confusion. They are called polynomials because they are polynomials of $\cos$. For example, $\cos(2x)=2\cos^2(x)-1\implies T_2(x)=2x^2-1$. $\endgroup$ – Simply Beautiful Art Dec 7 '16 at 0:03

They are called double angle formulas. It doesn't only work for sine, there's also cosine and tangent, so in general they are called double angle formulas.


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