# Cartesian to polar conversions

## Homework Statement

find polar coordinates of the points whose cartesian coordinates are given.

## Homework Equations

heres the point: (3sqrt(3), 3)

## The Attempt at a Solution

well i know that r^2 = (sqrt(a^2 + b^2))
so the answer here is : 6

and if we use tan(theta) = o/a = 3/(3sqrt(3)
so the answer here is: 1/sqrt(3)

so theta is pi/6

so how do i know its pi/6?

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benorin
Homework Helper
theta = arctan(1/sqrt3) = pi/6 (in radians, always radions for polar coordinates).

HallsofIvy
Homework Helper

## Homework Statement

find polar coordinates of the points whose cartesian coordinates are given.

## Homework Equations

heres the point: (3sqrt(3), 3)

## The Attempt at a Solution

well i know that r^2 = (sqrt(a^2 + b^2))
so the answer here is : 6

and if we use tan(theta) = o/a = 3/(3sqrt(3)
so the answer here is: 1/sqrt(3)
The right hand side of that equation, not the "answer" (to what question?!), is $\frac{1}{\sqrt{3}}$. In general, if you know what $tan(\theta)$ is, you can find $\theta$ by using the arctan function- perhaps on a calculator. Here, you are probably expected to know that $sin(\pi/6)= \frac{1}{2}$ and that $cos(\pi/6)= \frac{\sqrt{3}}{2}$ so that $tan(\pi/6)= \frac{1}{\sqrt{3}}$.

so theta is pi/6

so how do i know its pi/6?