A) Create a program that uses Taylor series approximation of 𝑦=sin(𝑥), between −2𝜋 and 2𝜋 with 𝑥𝑖=0 and ℎ=0.5,0.25,0.1 radians. Plot the errors, using 𝜖=𝑦−𝑦̂, for second and third order approximations. What difference do you notice between the errors? What is the average error? [25 Marks]
B) Change the program so that 𝑥𝑖 is updated with each new estimate for 𝑥𝑖+1 (recursively estimated) with ℎ=0.1. You will need to use the relationship cos(𝑥)=√(1−sin2(𝑥)). Plot the errors for the first and second order approximations. How do they compare the Part A? What are the sources of error?
I've done part A, bur for part B, I'm confused and dont know how to let xi updated with each new estimate for xi+1.
please give me some clues, thank you !