Trig Graphing

B= 4/8 C=4/8

I think there are a couple of different ways to take lthis question.

Looking at the graph I can see that  b=a+2pi

From a to b is a whole wavelength of  cos a   and a half a wavelength of cos (a/2)

This means that

1-d = c - - 1

1-d= c+1

c=-d

$cos\;a= \frac{1}{8}\\ cos(\frac{a}{2}+\frac{a}{2})=\frac{1}{8}\\ cos^2(\frac{a}{2})-sin^2(\frac{a}{2})=\frac{1}{8}\\ cos^2(\frac{a}{2})-(1-cos^2(\frac{a}{2}))=\frac{1}{8}\\ 2cos^2(\frac{a}{2})-1=\frac{1}{8}\\ 2cos^2(\frac{a}{2})=\frac{9}{8}\\ cos^2(\frac{a}{2})=\frac{9}{16}\\ cos(\frac{a}{2})=\pm\frac{3}{4}\\ \text{discount the positive answer}\\ c=cos(\frac{a}{2})=-\frac{3}{4}\\ $

$d=\frac{3}{4}$

huh. I never thought that you could prove c in terms of d
Thanks Melody!