How do you convert # r = 1 + 2sin(t)# to rectangular form?
1 Answer
Jun 12, 2017
Explanation:
Use the substitutions:
#r^2 = x^2 + y^2#
#y = rsintheta#
#x = rcostheta#
Now make substitutions when possible.
#r = 1 + 2sintheta#
#r^2 = r + 2rsintheta#
#x^2 + y^2 = sqrt(x^2+y^2) + 2y#
#x^2-2y+y^2 = sqrt(x^2+y^2)#
#(x^2-2y+y^2)^2 = (x^2+y^2)#
#(x^4-2x^2y+x^2y^2)+(-2x^2y+4y^2-2y^3)+(x^2y^2-2y^3+y^4)=x^2+y^2#
#x^4-4x^2y+2x^2y^2+4y^2-4y^3+y^4 = x^2 + y^2#
#x^4 -x^2 -4x^2y +2x^2y^2+3y^2-4y^3+y^4=0#
You could expand and simplify this further but this is a good stopping point.
Final Answer
