How do you create a Taylor expansion to solve sinx for values of x in degrees?

Please help me! I cant figure out how to solve this problem! I was able to convert x from degrees to radians, but I cant get my error tolerance to define or calculations of sin(x) for any x value.

The Taylor’s series expansion for sin x where x is in radians is:

sin(x) = summation of ((-1)^n)*x^(2*n+1)/factorial(2*n+1)

Write a Matlab script which calculates the sin of x by using the Taylor series expansion x specified in degrees. Calculate the sin of x using a while loop where the stopping criteria is the error E < 1x 10-6. E which is defined below is a function of the summation at the values of n (Sn) and n-1 (Sn-1).

E=abs((factorial(n)-factorial(n-1))/(factorial(n-1)))

As part of the problem your program should calculate the values of sin x at various values of x in degrees and tabulate using an fprintf statement as follows:

For x = 30:30:180 degrees, Calculate sin(x) and display both in a 2 column table

This is what I have so far. Does the code make sense?

clear

clc

%Problem 4 Hwk 1

%x degrees, must convert to radians first

n=25;

x=30:30:180;

x=angle_radians(x)

while E > 1*10^(-6)

for i = 0:n

y = ((-1)^i)*x^(2*i+1)/factorial(2*i+1);

end

sinx= summation(y)

Sn =sum(y)-y(n);

end

%fprintf('x(deg) | sin(x) \n', x, sinx)

%fprintf('x= %0.4f S= /n', n, sinx)

function x =angle_radians(x)

x=pi/180*x;

end

function E =stopValue(sinx,Sn)

E=abs(((sinx-Sn))/Sn);

sinx = sum(y);

Sn =sum(y)-y(n);

end

function sinx = summation(~)

y = ((-1)^i)*x^(2*i+1)/factorial(2*i+1);

sinx = factorial(y)

end

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[madhan ravi]

while E < 1E-6 
      % ^-—-—- change it

By the way have looked https://www.mathworks.com/help/symbolic/taylor.html ? Plus why do you create a custom function when there already exists a custom function deg2rad() ?

[Dylan Huss]

Thanks for the fix on the E value and the custom function deg2rad()! My main problem now is that E is an undefined variable. I dont know how to set it. I looked at the Taylor series help, and I got a function. But I have no idea if I used it right.

Here's the updated code

clear

clc

%Problem 4 Hwk 1

%x degrees, must convert to radians first

n=25;

x=30:30:180;

x=deg2rad(x)

while E < 1E-6

for i = 0:n

y(i)= ((-1)^i)*x^(2*i+1)/factorial(2*i+1);

sinx=Taylor(y)

Sn =sinx-y(n)

E=Error(n)

end

end

%fprintf('x(deg) | sin(x) \n', x, sinx)

%fprintf('x= %0.4f S= /n', n, sinx)

function E = Error(n)

Sn= sinx -y(n);

E=abs(((sinx-Sn))/Sn)

end

function sinx = Taylor(y)

y(i)= ((-1)^i)*x^(2*i+1)/factorial(2*i+1);

sinx = taylor(y,x)

end