question about Taylor Expansion

A) Create a program that uses Taylor series approximation of ?=sin⁡(?), between −2? and 2? with ??=0 and ℎ=0.5,0.25,0.1 radians. Plot the errors, using ?=?−⁡?̂, 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 ?? is updated with each new estimate for ??+1 (recursively estimated) with ℎ=0.1. You will need to use the relationship cos(?)=√(1−sin2(?)). 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 !

[James Tursa]

What code have you written so far? What specific problems are you having with it?