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##### Homework 1, Computing Sine and Cosine with Infinite Series;due via D2L dropbox by Thursday, September 13, at 11:55 pm;10 points;In...

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Homework 1, Computing Sine and Cosine with Infinite Series;due via D2L dropbox by Thursday, September 13, at 11:55 pm;10 points;In homework 1, we?re going to compute an infinite series (although we won?t go to infinity). Consider;the infinite series for sin(x), with x in radians. (The interval 0 to 2? radians is the same as 0 to 360;degrees.);();We can use a loop to compute this to varying degrees of accuracy. You?ll ask the user for the number of;terms to handle. I have posted a version of this as hw1-unsolved.txt. You will need to copy it and;rename your copy as..py. (Sorry, D2L won?t let me post.py files.);This file won?t run for you right off the bat, because the code for computing the terms is missing. But;everything else is there. You must add the comments at the top for your name, lecture, and recitation;and you must add unique, original comments to the code that computes the terms to explain your logic.;Comments in Python begin with a #.;You are free to use either the factorial I showed in class, or math.factorial(x).;Part 1 (7 points): write a Python function called infinite_sin_1. Here?s the first line;def infinite_sin_1(x);Tasks;First, you will need a variable for the total of these terms. Start that at 0.;Second, you will ask the user how many terms to use. The command for this is a little ugly;iterations = int(raw_input('Enter the number of cosine terms to add up: '));Here, the raw_input() command prompts the user for a string. But we need that string to;become an integer. So we use the int() command to change the string we get back from raw_input into;a number.;Third, you will want to write a for-loop that uses the range command to make a list of numbers;[0, 1, 2, 3, 4]. The for-loop also sets a counter variable called i to each of these numbers in turn. (Take a;look at the python examples from class to remember how for-loops work.);Fourth, inside this for-loop, you?ll figure out what the next term is and add it to the total.;Getting the right exponent/factorial numbers.;When i=0, the exponent and factorial for that term is 1.;When i=1, the exponent and factorial for that term is 3.;When i=2, the exponent and factorial for that term is 5.;Use i to calculate the exponent and factorial for each term.Getting the right sign for each term.;This series has alternating positive and negative terms.;When i=0, 2, or any even number, the term is positive.;When i=1, 3, or any odd number, the term is negative.;Use i to figure this out.;Adding the term to the total.;When you are getting the right terms, add each one to the total inside the loop.;At the end of the function, the last line should return the total. (Else, you will have no answer!);Fifth, use Python?s math.sin(x) to check your answer. You should be surprisingly close to the;right number after adding a few terms.;Part 2 (3 points). Write a similar method for infinite_cos_1(x). You will want to Google around for the;infinite series for cosine, which should look similar to the one you know for sine. This should require;only small changes inside the for-loop.;When I run this code and it works, I see output like this.;Enter the number of sine terms to add up: 3;Enter the number of cosine terms to add up: 6;real sine: 0.8660254037844385965883021;my sine 1: 0.8662952837868347355509968;my sine is accurate to: 0.0002698800023961389626947;real cosine: 0.5000000000000001110223025;my cosine 1: 0.4999999963909432243447384;my cosine is accurate to: 0.0000000036090568866775641;Extra credit (1 point): if you have this all working and you are bored, send me email about how bored;you are, and we?ll discuss a more efficient way to compute these series.

Paper#73431 | Written in 18-Jul-2015

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