Consider the following figure:
Compare the area of the triangle with the area of the sector to prove
Proof. Assume the radius is . For we have the triangle has base length and height the area is
The area of the circular sector is
Since the area of the triangle is less than the area of the sector we have,
Then, since we have for
, but since the in the specified range we get , as a result, it doesn't justify . Of course, with its very easy to solve.
Hi, thanks! Yes, that was definitely incorrect. I put up a fix now, and also corrected the typo in the diagram that had the origin labelled with $P$.
but we assume 0<x<pi/2 this would imply sinx<x for 0<x<pi which is not true