Drawing the sine curve: the length of a half chord
- Lee W Fisher
The word sine comes from a mistranslation of the Sanscrit word for Half Chord. 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. 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. When , we see that the y coordinate of point A is . We say, . The graph on the right has point C marked at . Move the slider for the angle to see how the y coordinate changes as the point A traces the circumference of the circle.
Use the applet to find the value of sin(122°)
Use the applet to find the value of sin(256°)
What other angle has the same half chord length AB as the angle 256°?