title: How to calculate sine and cosine without importing math?
body: <p>I started programming in python not too long ago and I am having trouble with a part of a program. The program will ask for input from the user and he can input: A, B, C, M, or Q. I have completed the A, M, and Q part but I can't figure out how to do the parts for B (calculate the sine of the number you want) and C (calculate the sine).
  All the information I was given was:</p>
  
  <blockquote>
    <p>The power series approximation for the sine of X can be expressed as:
    sine(X) = X – (X3/3!) + (X5/5!) – (X7/7!) + (X9/9!) .... Note that an
    individual term in that power series can be expressed as: (-1)k *
    X2k+1 / (2k+1)! where k = 0, 1, 2, 3, ….</p>
  </blockquote>
  
  <p>Oooh, and (but for this a while loop should do right?): 
  When computing the sine of X or the cosine of X, the program will expand the power series
  until the absolute value of the next term in the series is less than 1.0e-8 (the specified epsilon).
  That term will not be included in the approximation.</p>
  
  <p>And I can't use import math.
  Can anyone give me an idea of how I can do this? I sincerely have no idea of where to even start hahaha.</p>
  
  <p>Thanks in advance!</p>
  
  <p>***Hey guys, I've been trying to do this for the last 3 hours. I'm really new to programming and some of yours answers made it a bit more understandable for me but my program is not working, I really don't know how to do this. And yes, I went to speak with a tutor today but he didn't know either. So yeah, I guess I'll just wait until I get the program graded by my teacher and then I can ask him how it was supposed to be done. Thank you for all the answers though, I appreciate them! :)</p>