Solve each equation on the interval 0<= θ < 2n

1) sinē θ - cosē θ = 1 + cos θ

2) cos (2θ) + 6 sinē θ = 4

Thanks in advance guys.

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- Feb 4th 2008, 02:18 AMcloudzer0Trignometric equation help.
Solve each equation on the interval 0<= θ < 2n

1) sinē θ - cosē θ = 1 + cos θ

2) cos (2θ) + 6 sinē θ = 4

Thanks in advance guys. - Feb 4th 2008, 02:59 AMmr fantastic
1) Replace $\displaystyle \sin^2 \theta$ with $\displaystyle 1 - \cos^2 \theta$ and re-arrange to get a simple quadratic in $\displaystyle \cos \theta$:

$\displaystyle \cos \theta (2 \cos \theta + 1) = 0$.

Now solve $\displaystyle \cos \theta = 0$ and $\displaystyle 2 \cos \theta + 1 = 0$.

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2) Replace $\displaystyle \cos (2\theta)$ with $\displaystyle 1 - 2 \sin^2 \theta$ and re-arrange to get a simple quadratic in $\displaystyle \sin \theta$:

$\displaystyle \sin^2 \theta = \frac{3}{4}$.

Now solve $\displaystyle \sin \theta = \frac{\sqrt3}{2}$ and $\displaystyle \sin \theta = -\frac{\sqrt{3}}{2}$. - Feb 4th 2008, 03:42 AMcloudzer0
Thank you for your help, I actually worked it through and figured out those problems myself. However, there are still some confusions going on which I've been looking at for a good while.

Couple of other different problems.

Problem:

cos θ = sin θ

My work:

cos θ - sin θ = 0

=> (cosθ - sin θ)ē = 0

=> cosēθ - 2cosθsinθ + sinēθ =0

=> 1-2cosθsinθ = 0

I'm pretty much stuck at this point. Did I do something wrong?

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Another problem which I seem to have trouble with is:

(tan θ - 1)(sec θ - 1) = 0 - Feb 4th 2008, 04:19 AMmr fantastic
- Feb 4th 2008, 05:56 AMcloudzer0
1) cos (4θ) - cos (6θ) = 0

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Find real zeros. interval 0<= x < 2n

2) f(x) = 4 cosē x - 1 - Feb 4th 2008, 08:34 PMmr fantastic