For trigonometry, it is imperative to memorize a tool known as the Unit Circle. This is a circle with a radius of 1 and a center on the origin. The points on the circumference of the circle are the coordinates that you need to know.
When you see a trigonometric function such as sine (or sin(theta)) or cosine (or cos(theta)), it refers the point on the circumference of the circle that intersects the line coming from the origin at a given angle (theta) counter-clockwise from the axis between Quadrant I and Quadrant IV of the coordinate plane.
In this case, pi/3 refers to the angle in radians, an alternate unit of measurement for angles (pi rad = 180°) that is generally used in trigonometry. The point on the unit circle that is intersected by this line is (1/2, sqrt(3)/2). Finally, the function, sin(theta) returns a value equal to the y-coordinate of the point, giving us an answer of sqrt(3)/2.
In the future, you should memorize all the major points on the unit circle along with their reference angles and you'll be able to find these answers quickly.
