Problem 57983. Easy Sequences 109: Summation of Derivatives of a Trigonometric Function
A trigonometric function, , is defined as follows:
where: ; and
x is in radians.
In this problem we are asked to evaluate the following summation:
where: x is a real number;
n is an integer;
or the k-th derivative of T with respect to x; and
For example for and , we have:
Please present the final output rounded-off to 6 decimal places. Therefore the final answer is .
NOTE: Symbolic toolbox is not available to Cody players. It is possible to do numerical differentiation in Matlab without symbolic toolbox. Just make sure that the output would be accurate within 6 decimal places of the 'exact' value obtained using syms, as shown above.
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