Approximation of Sine Using Script

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Ben
Ben 2012-5-27
Hello. I made a script that approximates sin(x) using the series x - x^3.3! + x^5/5! - ..... It is (x = value you wish to approximate, n = number of terms for the approximation series):
function out = ApproxSin (x,n)
out = 0;
for k = 0:n-1;
out = out + (-1)^k * x^(2*k+1)/factorial(2*k+1);
end
y = sin(x);
percenterror = (abs((out - y)/y))*100;
It works well - I was able to make it display the amount of percent error based on how many terms were used in the equation.
What I want to try doing now is the opposite. I want an approximation of less or equal to 1%, and MATlab to be able to calculate the number of terms automatically to do so. I've been trying to use a while loop to do so:
function out = ApproxSin2 (x)
y = sin(x);
b = (1/100*y) + y
c = -(b-y)+y
k = 0
p = 0
while b < p < c
k = k+1
p = x + (-1)^k * x^(2*k+1)/factorial(2*k+1)
end
But this doesn't work and I'm not sure why it doesn't. I was wondering if someone could modify the code above slightly so that the "while loop" could work. Thanks for your assistance.

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回答（1 个）

Walter Roberson
Walter Roberson 2012-5-27
while b < p < c
means
while (b < p) < c
which means to compare b to p, get the value 0 (false) or 1 (true), and then compare that 0 or 1 to c.
while b < p & p < c
  1 个评论
Ben
Ben 2012-5-27
Alright, I tried it, but for some reason it still doesn't work.
From the code, I was trying to get a loop to keep going until p was within 1% from the actual answer (b was the actual value + 1% and c was the actual value - 1%).
When I run the code though it states "k = 0 and p = 0" and it stops; I wanted it to keep increasing "k" until p was between b and c, but the code just seems to stop at p = 0 (the entire "while" loop is somehow being skipped). What could I do to fix this?

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