The variation of the values of sine and Cosine


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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

Join P and P'. Triangles POM and P'OM are congruent.

\ PM = MP'. If PM = y then P'M = -y.

From the DPOM, sin q = y and cos q = x

In D P'OM, sin (-q) = -y and cos (-q) = x

Note:



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