Niven's Theorem
Niven's theorem states that if x/pi and sinx are both rational, then the sine takes values 0, +/-1/2, and +/-1.
Particular cases include
See also
Rational Number, Sine, Trigonometry AnglesExplore with Wolfram|Alpha
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References
Niven, I. M. Irrational Numbers. New York: Wiley, pp. 37-41, 1956.Schaumberger, N. "A Classroom Theorem on Trigonometric Irrationalities." Two-Year College Math. J. 5, 73-76, 1974.Referenced on Wolfram|Alpha
Niven's TheoremCite this as:
Weisstein, Eric W. "Niven's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NivensTheorem.html