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What is the method for solving cosine squared equations?

  1. Jul 27, 2012 #1
    I was just finishing my physics homework (don't worry this isn't a HW question, the homework is done) and the last calculation I had to do was cos2(θ) = 0.6. I just plugged this into my calculator to solve for me and got it right.

    Now I'm curious though. How would one solve this by hand?
     
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  3. Jul 27, 2012 #2

    berkeman

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    Take the square root of 0.6 by hand, and use cosine tables?
     
  4. Jul 27, 2012 #3

    haruspex

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    If you really mean 'by hand' (no calculator),
    cos(2θ) = 2 cos2(θ) -1 = 0.2 = sin(π/2 - 2θ)
    π/2 - 2θ ≈ 0.2
    θ ≈ π/4 - 0.1
    Check (by calculator): cos2(π/4 - 0.1) = 0.5993..
     
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