The radius of the circles in these apps is 1 unit. [br][br]Note how the chord length changes as the points travel around the circumference.

We say a chord subtends an angle at the center of a circle. [br][br]Note that as the chord length increases, the angle at the center increases.

While chord lengths (and half chord lengths) have been studied since [url=https://mathigon.org/timeline]Hipparchus in 150 BCE[/url], it is only recently that mathematicians have parked the circle on the Cartesian plane to think of all possible chords through vertical/horizontal chords.

The sine curve is the measurement of half of the vertical half chord, using half of the angle at the center.[br][br]Using half chords and half angles is useful. For one, we see that they generate all right angle triangles.[br][br]Below we see that at 30 degrees, the length of half of the vertical chord is 0.5. [br][br]The graph shows the point (30,0.5). [br][br]A scientific calculator in degree mode will say sin(30)=0.5[br][br]The scientific calculator will also say sin[sup]-1[/sup](0.5)=30 [i] (read, sin 'inverse' 0.5 equals 30).[/i]