Question

Why does 1/8cos(2y+6) become 1/8cos(arcsinx/4)?

Answer 1

No idea.

Was there some kind of diagram?
how is the y related to the x ?

starting with 1/8cos(arcsinx/4)

= 1/8cos(theta) where sin(theta) = x/4
then cos(theta) = √(16-x^2)/4
and
1/8cos(arcsinx/4)
= 1/8(√(16-x^2)/4)
= √(16-x^2)/32