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Absolute Degrees in Terms of One Circle Revolution

Date: 05/02/2002 at 13:04:02
From: Andrew
Subject: Absolute degrees - in terms of one circle revolution

I'm sure there's a simple answer but I can't find it, so here goes...

I have an angle of -6 degrees which I need to express in terms of a 
single 0-360 revolution. The simple solution is to add 360 degrees, 
which would give me the correct answer of 354 degrees. However, if the 
angle is 366 degrees I can't use that formula; in this case I now have 
to subtract 360 degrees to get the correct answer of 6 degrees.

This is simply done, but honestly is sloppy thinking, as it's my mind 
automatically doing an if-else statement.

Q. is there an algebra equation that can be applied to any degree 
where the output would be an absolute degree in terms of a single 
0-360 degree revolution?

I only have an angle; there are no other measurements.

Date: 05/02/2002 at 16:30:38
From: Doctor Peterson
Subject: Re: Absolute degrees - in terms of one circle revolution

Hi, Andrew.

You didn't cover even worse cases, such as 726 degrees, where you have 
to subtract a multiple of 360 degrees. But that suggests what is 
really going on here: you are finding a remainder.

The standard angle corresponding to a general angle A is the remainder 
upon division by 360 degrees. You have to be careful even here, 
because the remainder when you divide a negative number can be thought 
of in two different ways, and here you have to use the less obvious 
definition: divide the angle by 360 degrees, find the greatest integer 
less than the result, and subtract 360 times this from the given angle 
to get the "remainder." For example, for -6 degrees,

    -6 / 360 = -0.016...

    int(-6 / 360) = -1  [no, not zero, which is GREATER!]

    -6 - 360 * -1 = -6 + 360 = 354

while for 366 degrees,

    366 / 360 = 1.016...

    int(366 / 360) = 1  [here it's what you expect]

    366 - 360 * 1 = 366 - 360 = 6

Apart from the greatest-integer function, this is straightforward 
algebra. The only way to avoid it would be to just repeatedly add or 
subtract 360, depending on whether the angle is greater than 360 or 
less than 0.

- Doctor Peterson, The Math Forum 

Date: 05/02/2002 at 17:59:14
From: Andrew
Subject: Absolute degrees - in terms of one circle revolution

Works like a charm. I was doing something similar but it only worked 
for the positive numbers. Now I know why.

Thank you - that really helped.
Associated Topics:
High School Coordinate Plane Geometry
Middle School Terms/Units of Measurement

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