Difference between revisions of "Trigonometry Functions"
→Arcsine - Approximation by Taylor Series
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This approximation is very accurate (99.9% - 99.9999%) for angles of 45 degrees and higher. For smaller angles you can get a higher precision when you use a taylor series with 15+ iterations. | This approximation is very accurate (99.9% - 99.9999%) for angles of 45 degrees and higher. For smaller angles you can get a higher precision when you use a taylor series with 15+ iterations. | ||
== | == Approximation by Taylor Series == | ||
According to [http://www.wikipedia.org Wikipedia], arcsine can be found with this series: | According to [http://www.wikipedia.org Wikipedia], arcsine can be found with this series: | ||
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set arcsinz to (Wiki.z+(1/2)*(Wiki.z3/3)+(3/8)*(Wiki.z5/5)+(15/48)*(Wiki.z7/7)) | set arcsinz to (Wiki.z+(1/2)*(Wiki.z3/3)+(3/8)*(Wiki.z5/5)+(15/48)*(Wiki.z7/7)) | ||
More terms will increase accuracy. The larger the angle, the more terms are needed to get acceptable accuracy. As a rough guide use 3 terms for every 10° to get an accuracy of at least 1 decimal digit. | More terms will increase accuracy. The larger the angle, the more terms are needed to get acceptable accuracy. As a rough guide use 3 terms for every 10° to get an accuracy of at least 1 decimal digit. | ||
== Arccosine == | == Arccosine == | ||