SOLUTION: Use the first five terms of the trigonometric series to find the value of sin pi/12 to four decimal places.

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Question 236801: Use the first five terms of the trigonometric series to find the value of sin pi/12 to four decimal places.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The power series expansion for sin(x) is:
sin%28x%29+=+x+-+x%5E3%2F3%21+%2B+x%5E5%2F5%21+-+x%5E7%2F7%21+%2B+x%5E9%2F9%21 ...
Your problem is to use the first five terms, as you see them above, to find sin%28pi%2F12%29. Because of pi, the exponents and the factorials, this will be a calculation-intensive task. So get a calculator (or find a calculator program on your computer).

If you are clever enough and your calculator is capable enough you might be able to type the entire 5-term expression and get the answer. In case you have no calculator or in case you or your calculator are not quite up to the task of calculating the entire expression at once, I'm going to provide a step-by-step process:
  1. Calculate the factorials and write them down. Remember that n! is short for 1*2*...*n. So 3! = 1*2*3 = 6, 5! = 1*2*3*4*5 = 120, etc.
  2. Calculate pi%2F12 and write it down (or store it in your calculator).
  3. Calculate %28pi%2F12%29%5E3%2F3%21 and write down the result.
  4. Calculate %28pi%2F12%29%5E5%2F5%21 and write down the result.
  5. Calculate %28pi%2F12%29%5E7%2F7%21 and write down the result.
  6. Calculate %28pi%2F12%29%5E9%2F9%21 and write down the result.
  7. Use your saved results from above to calculate
  8. Round off the previous result to 4 decimal places and you have your answer.