The exponential function can be defined by the power series as: 80 sin(z) = Σ (-1)* k=0 (2k+1)! Z z5 2k+1 Z- + 3! 5! - 7! +... a) Using recursive function technique, write a function sinusoidal inputs: z and k. The function will output the corresponding value. your recursive function with z = 2 and k=3 >> sinusoidal (2,3) (z, k) that takes 2 In your script, test ans == 0.9079 b) Consider that z=1. Write a script that will loop through values of k until the difference between the series and the actual value (which is sin(1)) is less than 0.0001. The script should then print out the built-in value of sin(1) and the series approximation to five decimal places, and also print the value of k required for such accuracy.

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