Question

a particle moves along a circular arc of radius r making an anlge theta with the centre.the magnitude of displacement is

Answer 1

The triangle formed is an isosceles triangle with side OP=OQ=radius(R). Let the angle POQ be xx. 
Now using the Sine Law of Triangle, we can say:
OPsin(180∘−x2)OPsin(180∘−x2)= PQsinxPQsinx
and applying:
sin2Asin2A= 2sinA2sinA cosAcosA
We can have our desired result !!!
Also for very small angle sinxsinx=xx. So, the displacement reduces to: 
RxRx
Cheers.
*All Angles mentioned are in degrees. To convert into Radians Multiply the angle with π180