Approximation of Sine Using Script

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.

Answer 1

[Walter Roberson]

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

[Ben]

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?