# pheta, cos2pheta = 4cospheta, uncomplicated trig

## pheta, cos2pheta = 4cospheta, uncomplicated trig

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

**karooomph**- Posts : 74

Join date : 2008-11-19

Age : 23

Location : ubseikastan

## Re: pheta, cos2pheta = 4cospheta, uncomplicated trig

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.

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.

**bfrsoccer**- Administrator
- Posts : 61

Join date : 2008-11-09

## Re: pheta, cos2pheta = 4cospheta, uncomplicated trig

alrite, thanks bfr

**karooomph**- Posts : 74

Join date : 2008-11-19

Age : 23

Location : ubseikastan

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