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I'm sure there's a perfectly reasonable answer for this that I'm not seeing, but why does the output of asin() become complex for inputs greater than 1?
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what real angle do you expect to provide sine values > 1? |
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Originally Posted by: tedd  but why does the output of asin() become complex for inputs greater than 1 ? By math design of this function. BTW, it is fetched from Windows library. 
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Originally Posted by: mkraska what real angle do you expect to provide sine values > 1? The question I had in mind wasn't why asin() can't evaluate to a real number for inputs greater than 1 radian. It's why it evaluates to a complex number. It wasn't until I looked up the complex form of arcsin on Wikipedia that I knew there even was such a thing. I'm still struggling to visualize it. I guess that's what comes from being an engineer instead of a mathematician.
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Originally Posted by: tedd It's why it evaluates to a complex number. Cartesian maths relate x & y, thus solvable within mutual existence. Above 1 asin(x) is outside the Cartesian system. Thus, the alternate maths are complex, by nature inaccurate whereas there is no mutual relationship in blue sky. Even Cartesian maths may not be accurate when the mutual relationship confuse each other in infinitesimal values outside distinction. An example is the Goat radius. Mathematica 4.0 declares max 8 decimals. In Smath, this example is pretended ~ 12 decimals. There is another example function having too flat low region. Cheers ... Jean.  Maths asin(x).sm (7kb) downloaded 2 time(s).
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