Considering the Maclaurin series for cos x and starting with the simplest version, cos x = 1, add terms one at a time to estimate cos(/4) . After each new term is added, compute the true and approximate percent relative errors. Use MATLAB to determine the true value. Add terms until the absolute value of the approximate error estimate falls below an error criterion conforming to two significant figures.

Note:

Maclaurin series for cos x :

cosx=1-x22!+x44!-

Hint:

1. error criterion: 0.5*10^(2-sigfig)
2. Initialization of approximate percent relative errors: 100

## please write down comment for each steps briefly.