sinSeries ( angleInRadians ; series ; k )

sinSeries returns the sine of an angle as precise as you want, without the limitations of the built-in sine function

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Jeremy Bante
OshVay Systems, Inc.
http://www.oshvay.com/

Sample input:

SetPrecision(
sinSeries( 1; 0; 0);
400
)

Sample output:

.8414709848078965066525023216302989996225629881927640951426554576562466027361022992269087528874750932049961003819938774137825858326941363135636005387778464857227487290034458963420337622567171118102610920468850474707592770806914662577633187821606009639727005562578707021665451616489751832682881447162273246815366988330124600199519048486357691705405587764427230383550397413053247991229389088788789920977

Function definition: (Copy & paste into FileMaker's Edit Custom Function window)

/* sinSeries( angleInRadians; series; k) recursively adds the terms of a power series to compute the sine of an angle (in radians) to any precision that FileMaker is capable of. */

Let(
    [
    KthTerm = (-1)^k * angleInRadians^(2*k+1) / Factorial(2*k+1);
    KthSum = series + KthTerm
    ];

    Case(
        series = KthSum;
        KthSum;

        sinSeries( KthSum; k+1; angleInRadians)
    )
)

With FileMaker 7 came the capacity for storing numbers with 400 decimal digits of precision. However, FileMaker's built-in trigonometric functions still only evaluate to 16 places; sinSeries returns the sine of an angle [in radians] as precise as you want (with use of the SetPrecision function) by recursively adding the terms of a power series. The last two arguments to the sinSeries function are for the function's own use in recursive calls, and each should always be 0 when called by the developer.

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Note: these functions are not guaranteed or supported by BrianDunning.com. Please contact the individual developer with any questions or problems.

sinSeries ( angleInRadians ; series ; k )

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