Question

NOTE: Very useful trigonometric identities are these: sin(A B)-sin A cos B sin B cosA, cos(A +B)-COSA cos B-sin A sin B 32. (Bonus problem) A periodic function g(x)is defined on one period like this: g(x).0' on 1<x<0, and it equals x on 0<<1 (a) Give a labeled sketch of the graph of g(x), let's say from-1.5 to 3.5 (b) Give labeled sketches of, the graphs of g (x) and g(x) (i.e, the even and odd parts ofg).

Answer 1

In Delta OPM sin(A + B) = M P/O P = M R + R P/OP = MR/OP + RP/OP = QN + RP/OP = QN/OP + RP/OP = QN/ON . ON/OP + RP/PN . PN/OP = sin A cos B + cos A sin B Now using identity sin (90 - theta) = cos theta cos (A + B) = sin [90 - (A + B) = sin [(90 - A) + (- B)] = sin (90 - A) cos (- B) + cos (90 - A) sin (- B) = cos A . cos B - sin A . sin B since cos (-A) = cos A sin (- A) = -sin A g(x) = { 0 -1 < x < 0 x 0 < x < 1
trigonometric identities.. And periodic function