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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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