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sarm22 Group Title

can someone help solve cos(2x)+cos(4x)=0 x is really just theta

  • one year ago
  • one year ago

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  1. ZeHanz Group Title
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    Do you know the formula: cos(2x)=2cos²x-1? You use is to convert to a cosine of half the original angle. So you can also use it to convert cos(4x) to something with cos(2x).

    • one year ago
  2. ZeHanz Group Title
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    So you get: cos(2x) + 2cos²(2x)-1=0, or: 2cos²(2x) + cos(2x) - 1=0 This is a second degree polynomial: to see that better set cos(2x)=p: 2p² + p - 1 = 0. Solve it, and then remember that p = cos(2x), so solve for x then...

    • one year ago
  3. sarm22 Group Title
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    what happens to the one from changing the cos(2x) since its equal to 2cos^2x-1

    • one year ago
  4. ZeHanz Group Title
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    You don't have to change that one, so you get only cos(2x) everywhere in the equation. That makes it possible to consider it as a quadratic equation, with cos(2x) as a variable.

    • one year ago
  5. ZeHanz Group Title
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    So if you have 2p² + p - 1= 0, factor it as: (2p - 1)(p + 1) = 0. This gives p = 1/2 or p = -1. Now remember: cos(2x) = p, so we have to solve: cos(2x) = 1/2 and cos(2x) = -1. Try it. If you don't succeed, let me know!

    • one year ago
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