Does anyone has any reference that discusses why the Harmonic Addition Theorem called the R-formula in high school textbooks? I was guessing it is because of the way that it is generally represented as $a\sin x+b\cos x=R \sin (x+\alpha)$ there. Were there any other reason why the amplitude is denoted as $R$ though?
2026-04-01 06:07:39.1775023659
History of R-formula for trigonometry
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I learned in it High school exactly as stated by OP. Not in math, but in physics when studying the chapter "waves". For us, the $R$ indicated Range and in fact, it is the Range of $y=asinx+bcosx$ when graphed, and is given by $R=\sqrt{a^2+b^2}$. This is not immediately evident without converting left hand side to right hand side with some trigonometric input, which I think, is well known on MSE. And I introduce it this way in my trig class as well.