

It is clear from the diagram that the values of






2p.


Theorem 5
Statement:
For all values of q, cos (-q) = cos q and sin (-q) = -sin q
Proof:


Fig.(b)
Let XOX' and YOY' be the rectangular coordinate axes. With O as centre and radius unity draw a circle to cut x-axis at A and A' and y-axis at B and B'. Let the rotating line start from OA revolving in anticlockwise line from its starting position revolves in clockwise 
\ PM = MP'. If PM = y then P'M = -y.
From the DPOM, sin q = y and cos q = xIn D P'OM, sin (-q) = -y and cos (-q) = x

Note:


