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> Mike Sebastian maintains a page of “calculator forensics”, recording the result of computing arcsin(arccos(arctan(tan(cos(sin(9)))))) on as many different mod
by red_trumpet 4y ago
> Mike Sebastian maintains a page of “calculator forensics”, recording the result of computing arcsin(arccos(arctan(tan(cos(sin(9)))))) on as many different models of calculator as he or his pals can get their hands on. The value should be exactly 9
That's mathematically not correct. To define the function arcsin you have to choose a codomain, which is typically the interval [-pi/2, pi/2]. So for any values x not in that interval you will have arcsin(sin(x)) != x.
- fennecs 4y agoDynamic typing failures come up in math too. People love to ignore precisely where functions are defined, and then try to dynamically extend it elsewhere and are surprised when it spits out nonsense. Another example, saying a function has a non isolated singularity. It’s more like a codimension something region where you fail to glue together and get a coherent result.
- fiddlerwoaroof 4y agoI assume this is assuming degrees instead of radians? At least, iOS’s builtin calculator seems to use degrees by default.
- LegionMammal978 4y agoI believe this is referring to the trigonometric functions as calculated using degrees, in which the codomain of arcsin is [-90°, 90°]. Of course, the expression still violates dimensional analysis.
- amelius 4y agoIt's kinda obvious that this is using degrees, not radians.
- xigoi 4y agoIt definitely wasn't obvious to me — I wanted to point out the same thing.