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Decimal to Polar Coordinates

```
Date: 11/23/97 at 02:03:53
From: Michael Louis
Subject: Conversion from decimal to polar coordinates

The textbook I'm using for a PreCalculus course in night school shows
me how to convert polar coordinates into rectangular ones using the
formula:

x = r cos theta and y = r sin theta

I need to know how to convert in the opposite direction, from
rectangular coordinates back to polar.

Thank you.
```

```
Date: 11/23/97 at 05:09:48
From: Doctor Mitteldorf
Subject: Re: Conversion from decimal to polar coordinates

Dear Michael,

If you sum the squares of x and y, you find that you get r squared,
since sin^2 + cos^2 = 1 for any angle.  Therefore

r = sqrt(x^2+y^2)

To find theta, divide your two equations

y/x = sin(theta)/cos(theta) = tan(theta)

You can find theta from the inverse tangent function. You will need
to resolve the ambiguity about whether you have theta or (pi+theta)
by using the signs of x and y. For example, (x = 1, y = 1) means
theta = pi/4, but (x = -1, y = -1) means theta = 3pi/4, even though
the tangents of these two angles are the same.

-Doctor Mitteldorf,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Equations, Graphs, Translations

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