Realize the following approximation of the sin(x) function.. sin x ~ 00 L i=0 (-1)⁰ (2i + 1)! -x2i+1 = x x3 x5 x7 + 3! 5! 7! The approximation is based on the Maclaurin series expansion, and it becomes an equality (i.e. not only an approximation) as the summation continues to infinity. Your program will check if the approximation error falls below 1e-15, and stops if so. Otherwise, it will continue to a maximum of 100 summations. Your program should ask the user about the angle (in radians) which they want to find the sin() of. Notice that the user will only input an angle in radians and in the range [0-pi]. Use a while loop to answer the question. Use the following definition for the approximation error: Error = abs(true value - approximation) / true value Hint: you need two loops, where one goes through the summation, and the other is dedicated to calculating the factorials. Hint: The angle must be expressed in radians and must be in the range [0-pi]. Use such numbers when testing your code.

Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Realize the following approximation of the sin(x) function.. sin x ~ 00 L i=0 (-1)⁰ (2i + 1)! -x2i+1 = x x3 x5 x7 + 3! 5! 7! The approximation is based on the Maclaurin series expansion, and it becomes an equality (i.e. not only an approximation) as the summation continues to infinity. Your program will check if the approximation error falls below 1e-15, and stops if so. Otherwise, it will continue to a maximum of 100 summations. Your program should ask the user about the angle (in radians) which they want to find the sin() of. Notice that the user will only input an angle in radians and in the range [0-pi]. Use a while loop to answer the question. Use the following definition for the approximation error: Error = abs(true value - approximation) / true value Hint: you need two loops, where one goes through the summation, and the other is dedicated to calculating the factorials. Hint: The angle must be expressed in radians and must be in the range [0-pi]. Use such numbers when testing your code.
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