# What are the double angle trig formulas called?

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?

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