The word sine comes from a [url=http://www-math.ucdenver.edu/~wcherowi/courses/history2/hmsine.html]mistranslation[/url] of the Sanscrit word for Half Chord. [br][br]In the circle above (which has radius 1), we see a half chord, drawn from point A to the x axis. As we change the value of the angle alpha, the length of this half chord changes. The study of the lengths of these half chords is the origin of the sine function.[br][br]Notice that in the first quadrant and second quadrants, the length of the half chord is equal to the y coordinate of the point A. We define the sine of angle alpha to be the y coordinate of the point A.[br][br]When [math]{\Large \alpha=30}[/math], we see that the y coordinate of point A is [math]{\Large 0.5}[/math]. We say, [math]{\Large \text{sin}(30°)=0.5}[/math]. [br][br][br]The graph on the right has point C marked at [math]{\Large (30,0.5)}[/math].[br][br]Move the slider for the angle [math]{\Large \alpha}[/math] to see how the y coordinate changes as the point A traces the circumference of the circle.