sin(882955) is, to six decimal places, the same in degrees and radians.
@icecolbeveridge For how many numbers is the sin *exactly* the same in degrees and radians? I'd assume infinitely many.
@peterdrake (And has at least one zero, so it has infinitely many.)
@icecolbeveridge @peterdrake What’s the period?
@irving @peterdrake Oo, now I'm not sure it is. There are two families of solution, though, each of which recurs periodically. https://www.wolframalpha.com/input?i=f%28x%29+%3D+sin%28x%29+-+sin%28x*pi%2F180%29+
@irving @peterdrake \(\sin(x)- \sin\left(\frac{\pi x}{180}\right)= 2\cos\left(\frac{(180+\pi)x}{360}\right)\sin\left(\frac{180-\pi)x}{180}\right)\), I think, which gives you the two families as factors.
@peterdrake @icecolbeveridge And are any of those numbers rational? I'm guessing not.
@soaproot @peterdrake Correct, they're rational functions involving \( pi \). https://www.wolframalpha.com/input?i=sin%28x%29+%3D+sin%28x*pi%2F180%29+
@peterdrake Yeah, \( \sin(x^o)- \sin(x)\) is periodic.