The trigonometric function sin(zx) can be calculated by using the following seri
ID: 3274875 • Letter: T
Question
The trigonometric function sin(zx) can be calculated by using the following series The sin( x ) x + -+ a) What is the value of sin(2.17) by using the first three terms in the given series? b) What is the value of sin(2.17) by using the first four terms in the given series? c) Use your calculator for the true value of sin(2.17)? d) What is the true error for answer in part (a)? e) What is the absolute true error for answer in part (a). What is the relative true error for answer in part (a), g) What is the absolute relative true error for answer in part (a). h) What is the approximate error for answer in part (b)? i) What is the absolute approximate error for answer in part (b). j) What is the relative approximate error for answer in part (b). k) What is the absolute relative approximate error for answer in part (b), l) Assume that you do not know the exact value of sin(2.17), how many significant digits are at least correct if you use four terms in the series? m) What should be the pre-specified relative error tolerance if at least 4 significant digits are required to be correct in calculating sin(2.17)?Explanation / Answer
sinx = x - x^3/6 + x^5/120 - x^7/7!
a) sin(2.17) = 2.17 - 2.17^3 /6 + 2.17^5 /120
= 0.867922
b) using 4 terms
sin ( 2.17 ) = 2.17 - 2.17^3 /6 + 2.17^5 /120 - 2.17^7 /7!
= 0.822966
c) using calculator
sin (2.17) = 0.8257849931
d)
true error = 0.8257849931 - 0.867922 = - 0.0421370069
e) absolute true error = 0.867922 - 0.8257849931 = 0.0421370069
f)
relative true error =
= true error / true value value = 0.0421370069/ 0.867922 = 0.0485493
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