- #1

cbarker1

Gold Member

MHB

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I am having some trouble find the domain with this function: $f(x)=\frac{1}{\sqrt{x^2-2x\cos(\theta)+4}}$ and $\theta\in[0,\pi]$.

My attempt:

I know that the denominator needs to be greater than 0. So $\sqrt{x^2-2x\cos(\theta)+2}>0$. I squared both side of the inequality. Then I use the quadratic formula in terms of x: $x>\frac{2\cos(\theta)\pm\sqrt{4(\cos(\theta)^2-4}}{2}$. With some simplification and using the trig. identities, I got $x> \cos(\theta)\pm \sin(\theta)$. But I do not know how to proceed from here. Thanks,

Cbarker1