The 7th century Indian mathematician Bhaskara (c.600 – c.680) obtained a remarkable approximation for the sine function. Many subsequent ancient authors have given versions of this rule, but none provided a proof or described how the result was obtained. Grover  provides a possible explanation, but I think the rule can be explained more clearly. Rather than give the rule first, we will derive it, and then discuss its accuracy, and explore some alternative approximations. Our derivation is simply an exercise in modeling.
"Bhaskara’s approximation for the Sine,"
The Mathematics Enthusiast: Vol. 11
, Article 4.
Available at: http://scholarworks.umt.edu/tme/vol11/iss3/4