SOLUTION: if sin theta = radical 5 over 3 , then what does cos 2 theta equal ?

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Question 636444: if sin theta = radical 5 over 3 , then what does cos 2 theta equal ?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
We will be using the cos(2x) formula for this. There are three variations of this formula:
  • cos%282x%29+=+cos%5E2%28x%29-sin%5E2%28x%29
  • cos%282x%29+=+2cos%5E2%28x%29-1
  • cos%282x%29+=+1-2sin%5E2%28x%29
Any one of these three can be used. Often, choosing a particular one for a particular problem will make it easier. In this problem, since we already have sin(x), using the "all-sin" version, the third one, will make this problem easier. (The other two variations require that we have cos(x) which we do not yet have.)

So


P.S. It is not good to use the phrase "radical 5", even if your teacher uses it. Radicals are used to express all kinds of roots:
sqrt%285%29
root%283%2C+5%29
root%284%2C+5%29
root%285%2C+5%29
etc.
"Radical 5" could mean any of these. I had to guess that you meant square root. For square roots, say "square root" or just "sqrt". In the future, please post your questions in clear, unambiguous ways. Tutors are less likely to help if they are not even sure what the problem is.