Niven's theorem states that if 
and 
are both rational, then
the sine takes values 0, 
, and 
.
Particular cases include
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
Niven's Theorem
See also
Rational Number, Sine, Trigonometry AnglesExplore with Wolfram|Alpha
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 Web Resource. https://mathworld.wolfram.com/NivensTheorem.html