relative errors for the different solutions

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The sine function can be evaluated by the following series (based on the Taylor’s series expansion):
00
x3 x5 x
sin x = x – +
… =
3! 5! 7!
Σ».
(-1)
x(2n+1)
(2n + 1)!
n=0
where x is in radians.
a) Write a MATLAB program to compute the value of sin x up to a specified order term n
b) Compute sin 35° and sin 170° with n being 1, 2, 5, 7, 15
c) Compute the true and estimated percent relative errors for the different solutions, for example,
estimated relative error for n being 5 is computed from n being 4 and 5. Present the results in
both graphical and tabular format.
d) Do you see a systematic trend when comparing the true vs the estimated percent relative errors
for the numerical solutions?
e) What type of numerical error does this question illustrate? What is a viable remedy for this type
of numerical error?

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