What does the polar equation #cos2theta=1# represent?

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Answer 1 · 2017-03-30T05:05:41

#y=0#

Observe that #cos2theta=1#, when #theta=0# or #pi#. This is only on #x#-axis, whose equation is #y=0#. Let us work it out the other way.

The relation between polar coordinates #(r,theta)# and Cartesian coordinates #(x,y)# is given by

#x=rcostheta#, #y=rsintheta# and #r^2=x^2+y^2#

Hence #cos2theta=1# is #cos^2theta-sin^2theta=1#

or #x^2/r^2-y^2/r^2=1#

or #(x^2-y^2)=r^2=x^2+y^2#

or #2y^2=0# or #y=0# i.e. #x#-axis.