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pheta, cos2pheta = 4cospheta, uncomplicated trig

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pheta, cos2pheta = 4cospheta, uncomplicated trig

Post  karooomph on Sun Feb 08, 2009 9:59 am

What is the sum of the values of θ between 0 and 2π inclusive satisfying cos2θ = cos4θ?


Last edited by karooomph on Sun Feb 08, 2009 9:02 pm; edited 2 times in total
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Re: pheta, cos2pheta = 4cospheta, uncomplicated trig

Post  bfrsoccer on Sun Feb 08, 2009 1:20 pm

Although maybe you can use some trig identities to help you from the start in this problem, I think you would do something like:

1. cos2θ = cos4θ
1. Let some variable, like v, equal 2θ: cos v=cos(2v)
2. My TI-89 Titanium tells me that cos(2v)=2(cos v)^2-1, so: cos v=2(cos v)^2-1
3. Then, you can make another substitution and let w=cos v, and you end up with a quadratic equation: 2w^2-w-1=0
4. Solve for w, which will will then let you solve for values of v between 0 and 4pi (because v=2θ, and θ goes from 0 to 2pi), which then gives you values for θ, I think, which you can then add up

I think funion987 knows more about trig identities and stuff so he may have a better way of solving this problem.
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Re: pheta, cos2pheta = 4cospheta, uncomplicated trig

Post  karooomph on Sun Feb 08, 2009 3:53 pm

alrite, thanks bfr
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Term Papers

Post  monti on Wed Apr 28, 2010 6:33 am

It's great to see fresh, creative ideas that have never been done before.

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Re: pheta, cos2pheta = 4cospheta, uncomplicated trig

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