This Demonstration shows the relation between
, the measure
of the angle, and
, where
.
You can choose the measure of the angle
using the slider or by dragging the hypotenuse.
The length of the blue line is the sine of the angle (defined by the length of the green arc); the length of the orange line is the tangent of the same angle.
The blue line is always shorter than the green arc; therefore
.
Check the "compare…" button to compare the area of the yellow triangular region and that of the dark circular sector. The area of the triangle is equal to
; the area of the circular sector is equal to
.
