Do You Know Your Trig Graphs?

This becomes $\sin(x+\pi/3)+\sin(\pi/2-x-\pi/6)$

= $\sin(x+\pi/3)+\sin(\pi/3-x)$

= $2\sin(\pi/3) \cos x$

The amplitude of the above function is $2\sin(\pi/3) = \sqrt{3}$

The sum of any 2 sine or cosine wave with the same wavelength acquire maximum or minimum amplitude at their intersection. For instance, 2sin; 0 phase difference; intersect at 0; altitude=2sin(0). Another example, sin+cos; 90 phase difference; intersect at 45 deg; altitude=2sin(45). The problem above has phase difference of 60 degree. Therefore the altitude is 2sin(60/2). So the answer is 2*root(3)/2 = root(3). :)

Calculate f(0).