Question

re: reference angle - please explain the evaluation of 9pie/8-pie.

Answer 1

9pi/8 - pi = 9pi/8 - 8pi/8 = pi/8

so the angle 9pi/8 has the same magnitude of trig values as pi/8
because sin and cos can be determined using right triangles, the reference angle gives how far the angle is from the "x-axis"
the difference is the sign value which depends on which quadrant the angle is in