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

Question

4105 views around the world

You can reuse this answer
Creative Commons License

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.

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