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sarm22
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can someone help solve cos(2x)+cos(4x)=0
x is really just theta
 one year ago
 one year ago
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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ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
Do you know the formula: cos(2x)=2cos²x1? 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

ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
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

sarm22 Group TitleBest ResponseYou've already chosen the best response.0
what happens to the one from changing the cos(2x) since its equal to 2cos^2x1
 one year ago

ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
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

ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
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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