Find HRC and HRS where a is a real number Fx cos 2x 0 Solut

Solution

Here f(x) = Cos(2x) when 0< x</2 and

= 0 /2<x<

If we draw the graph of it for x = 0, f(x) = 1; x = /4, f(x) = 0 and x = /2, f(x) = -1

So f(x) = Cos2x lies between -1 and +1.

Now for f(x) = Sin (x/a); when x = 0 , f(x) = 0, x = a/2, f(x) = 1 and x =a, f(x) = 0

and after x>a, f(x) = 0.

So f(x) = sin(x/a) lies between 0 and 1.