Question

Implement MATLAB code that calculates sin(x) using the following formula, and measure the absolute error from the MATLAB provided function. The Taylor's formula is given as follows: sin(x) = 0+12 + 0x² + 5123 + 0.x4 + ... 23 25 27 -3! + 5- 7 + ... Plot both (1) the approximated value, and (2) absolute error. The following example uses x = 3 * pi, and k = 50. You may choose your own x, and k values. Approximation: Red with circle, Error: Blue.

Answer 1

x=3*pi;%change this as needed
k=50;%change this as needed
%assuming k is the number of terms

exact=sin(x);
sinx=zeros(1,k);
sinx(1)=x;%store approximation for every value of k from 1 to 50
for i=2:k
sinx(i)=sinx(i-1)+(x)^(2*i-1)*(-1)^(i+1)/factorial(2*i-1);
end
err=abs(sinx-exact);
plot(1:k,sinx,'ro',1:k,err,'b')
legend('approximation','absolute error')
grid on

x=3*pi;%change this as needed k=50;%change this as needed %assuming k is the number of terms CON 1000 o approximation - absolute error 800 1 1 1 1 1 exact=sin(x); sinx=zeros (1,k); sinx(1)=x;%store approximation for every value of k from 1 to 50 for i=2:k sinx(i)=sinx(i-1)+(x)^(2*i-1)*(-1)^(i+1)/factorial(2*1-1); end err=abs(sinx-exact); plot(1:k, sinx, 'ro', 1:k, err,'b') legend('approximation', 'absolute error') grid on 1 1 - 1 0 -200 -400 -600 -800 -1000 no 10 20 30 40 50