Question about Texas Instruments TI-30XA Calculator
Before using the inverse trigonometric functions, make sure your calculator has the right unit as angle unit. The unit of the values returned by the inverse trigonometric functions is the same as the default angle unit. This being said, you access the arcsine function by pressing 2nd sin^-1
The syntax is as follows number 2nd sin^-1 =
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Posted on Dec 09, 2009
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Posted on Jan 02, 2017
The sine of 6pi is indeed zero. The calculator works with twelve decimal digits while pi is an irrational number with an infinite number of decimal digits. Thus the calculator cannot actually calculate the sine of 6pi, instead it calculates the sine of 18.8495559215. The sine of that number is close to zero but not quite, about 0.000000000002 which is what the calculator shows. This is a natural consequence of using finite machines to deal with infinite numbers.
In degrees, 3*360 is 1080 exactly and thus the calculator can produce an answer of exactly zero.
You'll notice that the calculator also gives a nonzero result for the sine of 4pi.
The "proper" fix for this is something called "argument reduction." If the argument lies outside the range of 0 to 2pi (or alternatively, the range -pi to pi), add or subtract multiples of 2pi until the argument is inside the range. So in this case, subtract 6pi from 6pi to get zero, then take the sine of that.
Bear in mind that argument reduction won't always work, since it too is limited to twelve-digit arithmetic.
Posted on Dec 12, 2010
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