Question

The cos(x) function can be represented in a Taylor series shown below:

Write a Matlab program, and use a while loop, to calculate cos(150) (the input is in degrees) by adding terms of the series and stopping when the absolute value of the term that was added last is smaller than 0.0001.

Make sure to make the required degree <-> radian conversions.

Use fprintf to print the cos(150) (up to 2 decimal places) and the number of terms used to calculate it. Also, calculate and print the cos(150) using matlab's built-in function cosd. (Your code and the cosd function should return the same values).

• Create your script in matlab, name it Lab6.m and attach it in the space below. Your script should have a line of comment with your name and date and a line with a short description about the code.

Answer 1

Code Screenshot :

Executable Code:

result = 1;
angle = 150*(pi/180);
numerator = angle*angle;
denominator = 2;
sign = -1;
degree = 2;
count = 1;
while(numerator/denominator >= 0.0001)
   result = result + sign*(numerator/denominator);
   sign = -sign;
   numerator = numerator * angle * angle;
   denominator = denominator * (degree+1) * (degree + 2);
   degree = degree + 2;
   count = count + 1;
end

fprintf("%.2f is the value of cos(150) by Taylor series and total of %d terms is used\n",result,count);
fprintf("%.2f is the value of cos(150) by cosd in-build function\n",cosd(150));

Sample Output :

Please comment below if you have any queries.