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leftfield

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leftfield

- #2

enigma

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They come into play because the sin's are the same when mirrored across the y axis, the cos's are the same when mirrored across the x axis, and tangents are the same when rotated by 180 degrees.

Try putting in a few lines of code to catch what quadrant the angle is in.

For example (pseudocode):

Performing acos function

If quadrant = 3 or 4

->angle = 360-acos

else

->angle = acos

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HallsofIvy

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Generally computer or calculator "arc-functions" will give you the value closest to 0: for sin<sup>-1</sup>, between -[pi]/2 and [pi]/2, for cos<sup>-1</sup>, between 0 and [pi].

if [theta] is the value your computer program gives for sin<sup>-1</sup> then [pi]/2- [theta] is also a value- and of course, you can add any multiple of 2 pi to those.

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leftfield

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Hurkyl

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What programming language are you using? And can you post the code snippet you're using to compute the result?

Anyways, one alternative is to use the arctan function and trig identities to get the answer for arcsin. Here is the general procedure for deriving this type of identity:

arcsin (x) is the measure of the angle of the triangle with opposite side x and hypotenuse 1. (because sin y is opposite over hypotenuse)

Such a triangle has adjacent side sqrt(1 - x * x)

since tangent is opposite over adjacent, the same angle is given by:

arcsin x = arctan(x / sqrt(1 - x * x))

Or, you could try the taylor series for arcsin:

arcsin(x) = x + (1 / 2) * (x^3 / 3) + ((1 * 3) / (2 * 4)) * (x^5 / 5)

+ ((1 * 3 * 5) / (2 * 4 * 6)) * (x^7 / 7) + ...

Anyways, one alternative is to use the arctan function and trig identities to get the answer for arcsin. Here is the general procedure for deriving this type of identity:

arcsin (x) is the measure of the angle of the triangle with opposite side x and hypotenuse 1. (because sin y is opposite over hypotenuse)

Such a triangle has adjacent side sqrt(1 - x * x)

since tangent is opposite over adjacent, the same angle is given by:

arcsin x = arctan(x / sqrt(1 - x * x))

Or, you could try the taylor series for arcsin:

arcsin(x) = x + (1 / 2) * (x^3 / 3) + ((1 * 3) / (2 * 4)) * (x^5 / 5)

+ ((1 * 3 * 5) / (2 * 4 * 6)) * (x^7 / 7) + ...

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leftfield

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