Why is sin(20) = sin(160) = -sin(200) = -sin(340)?

Because they're all the same distance from the x axis on a coordinate plane. Also, remember that in quadrant I, all trig values are positive. In Q II, only sine and cosecant are positive. In Q III, only tangent and cotangent are positive. In Q IV, only cosine and secant are positive. Think of it as All Students Take Calculus.

The decimal expansion would be .27 repeated