Question

Assume we know the following:

cos(22.5 degrees)= sqrt(2+sqrt2)/2
sin(22.5 degrees)=sqrt(2-sqrt2)/2

cos(18 degrees)=sqrt((sqrt5+5)/8)
sin(18 degrees)=(sqrt5-1)/4

What is:
Sin(82.5 degrees)
cos(82.5 degrees)
sin(12 degrees)
cos(12 degrees)

Answer 1

using the same addition formulas as before, note that

82.5 = 60 + 22.5
12 = 30-18