How do you find the points of intersection of #r=1+costheta, r=3costheta#?

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Answer 1 · 2018-02-18T09:40:05

#theta=2npi+-pi/3 "form the general solution when n takes values "#
#........-3,-2,-1,0, 1, 2, 3,....... #

#"Given:",#

#r=1+costheta#

#r=3costheta#

#"To find the points of intersection , Equate rhs"#

#1+costheta=3costheta, #
#3costheta-costheta=1#

#2costheta=1#

#costheta=1/2#

#cos(pi/3)=1/2#

#theta=pi/3, " forms the primary solution"#

#costheta "is positive in 1st and 4th quadrants"#

ie

#theta=2npi+-pi/3 "form the general solution when n takes values "#
#........-3,-2,-1,0, 1, 2, 3,....... #