Question

How do you determine the polar coordinates for the intersection point(s) of the following polar equations: `r = 1` and `r = 2 \cos \theta`?

Answer 1

You can substitute `r=1` in the second equation `r=2cos(theta)` and you'll get:

`1=2cos(theta)` and
`cos(theta)=1/2`
There are two angles with `cos` equal to `1/2`;
`theta_1=60°` and `theta_2=300°`.

The coordinates of your points are then:

`(1;60°)` and `(1;300°)`