Re: [MacPerl] Trig Trouble

["Richard L. Grubb" <richard.l.grubb@boeing.com>]

Aiken, Greg wrote:
> 

> Note that for 'input' angles (ie, column 1 values) of 0 through 'less than
> 180', the angle returned by 'atan2' (ie, the last column) EXACTLY MATCHES
> the 'input' angle (ie, column 1 exactly matches the last column).
> 
> Note that for 'input' angles of 180 through 360, the angle returned by
> 'atan2' DOES NOT MATCH the 'input' angle (ie, column 1 does not exactly
> match the last column).
> 
> My questions are;
> 
> 1. Why is this happenning?

Because the returned angle from atan2 can be reported as either a
positive angle or a negative angle. The function has been programmed to
return the value that has the smallest absoulute value. For example, 345
degrees is equivalent to -15 degrees. Since 15 is smaller than 345, the
programmer assumed that the user would prefer to see the answer as -15
rather than 345. It is an arbitrary choice, but a faily standard one if
you delve into numerical standards.

> 
> 2. Would it be incorrect of me to assume (just because it looks so in this
> sparse sample data set) that if I constrain my evaluations to be in the
> range of 0 through 90, that I will always have EXACT results, or does the
> possibility of error still exist, even though it is not evident from this
> sparse sample data set?

I don't think your results are as exact as the printout implies. You
have a rough approximation for pi (22/7).
When the angle gets returned as a negative value, your print format
breaks down, and more accuracy is displayed.

But if you were using a sufficiently accurate value of pi, the results
in the 0 through 90 range (as well as the 0 through 180 range) would
come back with same value that was started with.
> 
> 3.  How have others traditionally solved this problem?

If you don't want negative angles returned, then add 360 to the result
if the result < 0.

> 
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-- 
Richard L. Grubb
Boeing Wichita

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