Re: trig. formula Question

In article <dq43qd$2k0$1@xxxxxxxxxxxxxxxxxxxxxxxxxx>,
Dave Seaman <dseaman@xxxxxxxxxxxx> wrote:
>On 11 Jan 2006 14:45:07 -0800, incon wrote:
>> HI I have looked everywhere I can and I cannot find the formula for the
>> trigonomic functions
>> Cosine
>> Sine
>> Tangent
>> Inverted Cosine
>> Inverted Sine
>> Inverted Tangent
>> I can do these on a calculator any day but I couldn't do them with out
>> one.
>> I figured you guys would know seeing as seems you all are a bunch of
>> math guros.
>> Thanks
>
>The "formulas" are transcendental and may not be of much help to you, but:
>
>sin(x) = (e^(i*x) - e^(-i*x)) / (2*i) = x - x^3/3! + x^5/5! - x^7/7! + ...
>cos(x) = (e^(i*x) + e^(-i*x)) / 2 = 1 - x^2/2! + x^4/4! - x^6/6! + ...
>tan(x) = sin(x) / cos(x)
>
>and the other 3 are just the inverses of those.

A simple series for atan that converges for |x| <= 1 is

atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...

convergence for all x can be achieved with

x
atan(x) = 2 atan( --------------- )
1 + sqrt(1+x^2)

We can get asin and acos using the following:

x
asin(x) = 2 atan( --------------- )
1 + sqrt(1-x^2)

x
acos(x) = pi/2 - 2 atan( --------------- )
1 + sqrt(1-x^2)

Rob Johnson <rob@xxxxxxxxxxxxxx>
take out the trash before replying
.

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