The solution
from the given: Polar coordinates #(1, (23pi)/8)#
Let #r=1# and #theta=(23pi)/8#
#x=r cos theta# and #y=r sin theta#
Let us solve for #x#
#x=r cos theta#
#x=(1)cos ((23pi)/8)#
#x=(1)cos ((16pi)/8+(7pi)/8)#
#x=(1)cos (2pi+(7pi)/8)#
use the sum formula #cos (A+B)=cos A*cos B- sin A* sin B#
#x=(1)[cos (2pi)*cos((7pi)/8)-sin (2pi)*sin((7pi)/8)]#
#x=(1)[1*cos((7pi)/8)-0*sin((7pi)/8)]#
#x=(1)cos((7pi)/8)#
#x=cos((7pi)/8)=-0.9238795325#
Let us solve for #y#
#y=r sin theta#
#y=(1)sin ((23pi)/8)#
#y=(1)sin ((16pi)/8+(7pi)/8)#
#y=(1)sin (2pi+(7pi)/8)#
use the sum formula #sin (A+B)=sin A*cos B+ cos A*sin B#
#y=(1)[sin (2pi)*cos((7pi)/8)+cos (2pi)*sin((7pi)/8)]#
#y=(1)[0*cos((7pi)/8)+1*sin((7pi)/8)]#
#x=(1)*sin((7pi)/8)#
#x=sin((7pi)/8)=0.3826834324#
God bless....I hope the explanation is useful.
