A calculus problem by Rob Matuschek
Calculus
Level
3
Having to rely on only his 4 function calculator for the college entrance exam, Alex knew he could use how many terms of a Maclaurin polynomial to approximate the sine of any angle in a given triangle to the nearest thousandth?
3
2
4
5
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1 solution
For any obtuse angle x , he could could use ( p i − x ) , thus the largest angle he would be dealing with is p i / 2 . The Maclaurin Polynomial for sine is an alternating series, thus the error bound for such an nth degree polynomial will be specifically the n+1 term. Since ( p i / 2 ) 9 / 9 ! < 0 . 0 0 1 < ( p i / 2 ) 7 / 7 ! , the first four terms suffice.