# Need help changing an irrational number into a rational number, involving polar coord

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• Apr 28th 2011, 06:27 AM
colorado
Need help changing an irrational number into a rational number, involving polar coord
I am working with problems of changing from Polar to Cartesian coordinates.

the problem is (-5, pi/3)
I know x=-5cos pi/3 = -5/2
and y = -5sin pi/3 \approx 4.33 or = 5sqrt3/2 but I only know that it can be written as 5sqrt3/2 because after I got 4.33 I check the answer. I need to know how to convert numbers like 4.330127019 in 5sqrt3/2

thanks!
• Apr 28th 2011, 06:43 AM
colorado
or another exmaple pi + tan^-1 (-1) approx 2.35619 or 3pi/4 (done in radians)
• Apr 28th 2011, 07:04 AM
topsquark
Quote:

Originally Posted by colorado
or another exmaple pi + tan^-1 (-1) approx 2.35619 or 3pi/4 (done in radians)

Apart from recognizing a few common ones, ie 1.570796... = pi/2, I think you will just have to rely on the trigonometry.

Also, please note that expressions like $\frac{5 \sqrt{3}}{2}$ are not rational numbers. A better description of what you are trying to say is probably "closed form" or "in the form of a fraction."

-Dan
• Apr 28th 2011, 07:10 AM
colorado
okay, hopefully approx values will work. Do you know where I might find a list of common ones? If not I'll try to find one. Thanks for the reply!!!
• Apr 28th 2011, 07:20 AM
topsquark
Quote:

Originally Posted by colorado
okay, hopefully approx values will work. Do you know where I might find a list of common ones? If not I'll try to find one. Thanks for the reply!!!

Frankly I don't even try to remember the approximate forms. If I have a decimal number that I need to, say, find the inverse sine of I let my calculator deal with it. (Nod)

-Dan