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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?
  2. jcsd
  3. Jul 27, 2012 #2


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    Staff: Mentor

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


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    Science Advisor
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    Gold Member

    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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