Question

given that cos 5pi/9 = sin y first express 5pi/9 as a sum of pi/2 and a angle and then apply a confunction identity to determine the measure of angle y

Answer 1

5/9 = 1/2 + 1/18
The co- in cosine means sine of the complement. That is
cos(x) = sin(pi/2 - x)
so, cos(5pi/9) = sin(pi/2 - 5pi/9)