- #1

cbarker1

Gold Member

MHB

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- Homework Statement
- Find the domain of this Function:

- Relevant Equations
- Quadratic Formula, Trig. Identity.

I am having some trouble find the domain with this function: ##f(x)=\frac{1}{\sqrt{x^2-4x\cos(\theta)+4}}## and ##\theta\in[0,\pi]##.I know that the denominator needs to be greater than 0. So ##\sqrt{x^2-4x\cos(\theta)+4}>0##. I squared both side of the inequality, ##x^2-4x\cos(\theta)+4>0##. Then I use the quadratic formula in terms of x: ##x>\frac{4\cos(\theta)\pm\sqrt{16(\cos(\theta)^2-16}}{2}##. With some simplification and using the trig. identity, I got ##x> 2\cos(\theta)\pm 2\sin(\theta)##. But I do not know how to proceed from here.

Thanks,

cbarker1

Thanks,

cbarker1

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