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.
