Use the unit circle to show: cos(theta) = sin(theta + pi/2)

Question

Use the unit circle to show that those two trigonomic idendities are equal. I am so lost

Answer 1

Draw a circle of radius 1 centre O, and draw two diameters at right angles, AOB and COD, dividing the unit circle into quadrants, COB, BOD, DOA, AOC. Draw a radius OX at angle x to OB. Also draw another radius OY at angle x to OC. Angles YOC and XOB=x. Also, YOB=90+x=(pi)/2+x.

Drop a perpendicular XP from X on to OB. OP=cosx.

Drop a perpendicular YQ to AO. SinYOA=sinYOB=sin((pi)/2+x)=YQ. Right-angled triangles YOQ, YOC and XOP are congruent and YQ=OP=cosx=sin((pi)/2+x).