Problem 1 The following infinite series can be used to approximate e 6 1 Write a

Question

Problem 1 The following infinite series can be used to approximate e 6 1 Write a program to approximate the value of cos x as follows: Using a loop you will add one more term to the approximation each iteration of the loop until your approximation is correct out to 5 significant figures. You may start off with your approximation equal to 1. Because we are starting off with the approximation equal to 1 this is our initial old value. Requirements: x must be entered using the input command Output should be as follows: The approximate value of cos (entered value) is f. ### It took # iterations to converge! 1. 2.

Explanation / Answer

X = input("Enter vulue of X=")
cos_x = 0; % intialization of approximate value

i =0:2:10000;

for k = 1:1:length(i) % this for loop for iteration
cos_x = cos_x +( ((-1)^(k+1))*(X^i(k)) )/( factorial(i(k)) );
cos_x
if ( abs((cos(X)-cos_x)) <= 10^-6) % this condition for accuracy
    break;
end

end

printf("Approximate value of cos(%f) is %f ", X,cos_x)
printf("It took %d iteration to converge ", k)

Output:-

Enter vulue of X=pi/3
X = 1.0472
cos_x = 1
cos_x = 0.45169
cos_x = 0.50180
cos_x = 0.49996
cos_x = 0.50000
Approximate value of cos(1.047198) is 0.500000
It took 5 iteration to converge

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