For this problem, you can use native Python, as well as the math, numpy, and mat-plotlib libraries.

Problem 1 - Structured Programming: Functions and Loops The infinite series for the cosine function is: cosx=i=0n(1)i(2i)!x2iorcosx=0!x02!x2+4!x46!x6+ Write a function called cosine that uses this formula to calculate the value of the cosine given x and the number of terms n. Define and use a separate function called factorial to calculate the factorial of x. Next, test the accuracy of the infinite series with respect to n for x=75 deg (note the units). Within your Python script, use a for loop to compute cos(x) as n varies from 1 to 6 . Each result should be printed with only six decimal places. Finally, comment on what value of n is needed to converge the cosine of 75 deg up to four significant figures