How do you convert $y = -3$ to polar form?

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Answer 1 · 2018-05-19T11:04:40

$rsintheta=-3$

Imagine we have a point $P$ with Rectangular (also called Cartesian) coordinates $(x,y)$ and Polar coordinates $(r,theta)$ .

The following diagram will help us visualise the situation better:

![https://keisan.casio.com/exec/system/1223526375]( useruploads.socratic.org )

We can see that a right triangle is formed with sides $x$ , $y$ and $r$ , as well as an angle $theta$ .

We have to find the relation between the Cartesian and Polar coordinates, respectively.

By Pythagora's theorem, we get the result

$r^color(red)2=x^color(Red)2+y^color(red)2$

The only properties we can say about $theta$ are its trigonometric functions:

$sintheta=y"/"r=>y=rsintheta$
$costheta=x"/"r=>x=rcostheta$

So we have the following relations:

${(r^2=x^2+y^2),(y=rsintheta),(x=rcostheta):}$

Now, we can see that saying $y=-3$ in the Rectangular system is equivalent to say

$color(blue)(rsintheta=-3)$

Answer 2 · 2018-05-19T11:08:10

$r=-3/sintheta$

$"to convert from "color(blue)"cartesian to polar"$

$•color(white)(x)x=rcostheta" and "y=rsintheta$

$rArrrsintheta=-3rArrr=-3/sintheta$

How do you convert y = -3y = -3 to polar form?