Question

How do you find the polar coordinates given the rectangular coordinates (1,sqrt3)?

Answer 1

`(1, sqrt(3))` in rectangular coordinates is `(2, pi/3)` in polar coordinates.

Explanation:

To translate rectangular to polar coordinates we use the follow:
`x=r cos(theta)`
`y=r sin(theta)`

From your question we can set up the equations:
`1=r cos(theta)`
`sqrt(3)=r sin(theta)`

Solve these simultaneous equations by division first:
`sqrt(3)/1 = sin(theta)/cos(theta)`
`sqrt(3) = tan(theta)`
`theta = pi/3`

Now substitute to find `r`:
`1=r cos(pi/3)`
`1=r 1/2`
`2=r`