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livin325

гæ (³õÈëÎÄ̳)

[ÇóÖú] Sine Approximation ÒÑÖªangle&ãÐÖµ£¬·µ»ØtermsÖµ

ÊäÈëÁ½¸ö²ÎÁ¿X ºÍ threshold. Öð½¥Ìí¼ÓtermsÖµ,Ö±µ½Âú×ã
abs£¨(true &#1048576;-approx)/true)< threshold ;
true ÊÇϵͳbuilt-in ·½³Ìʽsin(x)¡£
sin(x) = x &#1048576;- x^3/3! + x^5/5! - x^7/7!+...   
·½³ÌʽҪ·µ»Ø2Öµ¡£ approxºÍterms£¨Ìí¼ÓÁ˼¸¸öÊý£©
ÊäÈëX=pi/5, threshold=1e-6ʱ£¬ÏÔʾÈçÏ£º
>> format long
>> x = pi/5;
>> threshold = 1e-6;
>> [approx, terms] = approx_sine(x, threshold)
approx =
0.587785210384344
terms =
3
ÒÔÏÂÊDZ¾ÈË·½³Ìʽ£º
function [approx, terms] = approx_sine(x, threshold)
approx = x; % ³õʼ approximation
terms = 0; % Number of additional terms added to improve the approximation

while threshold > abs((sin(x)-approx)/sin(x))
   terms = terms + 1;
   approx = approx + (-1)^(terms)*x.^(2*terms+1)/factorial(2*terms+1)
end
end
ÇëÖ¸µã£¬ÎªÉ¶·µ»Øapprox´íÎ󣬶øÇÒ»¹Ã»·µ»ØtermsÖµ£¨ÇëʹÓÃwhile loop½âÌ⣩
>> sine function(pi/5, 1e-6)
approx =
   1.256637061435917
ans =
   1.256637061435917
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livin325

гæ (³õÈëÎÄ̳)

²»ºÃÒâ˼ÂÒÂëÇøÖØÐÂÊäÈëÈçÏÂ
abs((true-approx)/true)<threshold

sin(x)=x- x^3/3! + x^5/5! - x^7/7!+...
2Â¥2015-12-02 05:49:27
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
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