To find cartesian form of #(r,theta)# we use the formula
#x=rcos(theta)# and #y=rsin(theta)#
We are given the #(7, (23pi)/3)#
#r=7# and #theta=(23pi)/3#
Let us simplify this #(23pi)/3# into something which is easier to handle.
#(23pi)/3 + pi/3 = (24pi)/3#
#(23pi)/3 + pi/3 = 8pi#
#(23pi)/3 = 8pi-pi/3#
Also note #cos(2npi-theta) = cos(theta)#
and #sin(2npi-theta) =-sin(theta)#
#x=rcos(theta)#
#x=7cos(8pi-pi/3)#
#x=7cos(pi/3)#
#x=7(1/2)#
#x=7/2#
#y=rsin(theta)#
#y=7sin(8pi-pi/3)#
#y=7(-sin(pi/3))#
#y=-7(sqrt(3)/2)#
#y=-(7sqrt(3))/2#
#(7/2, -(7sqrt(3))/2)#
