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sarm22
 2 years ago
can someone help solve cos(2x)+cos(4x)=0
x is really just theta
sarm22
 2 years ago
can someone help solve cos(2x)+cos(4x)=0 x is really just theta

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ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1Do 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).

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1So 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...

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

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1You 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.

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1So 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!
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