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Math Help - Help finding the domain of a multivariable function

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    Help finding the domain of a multivariable function

    Find the domain of the function
    f(x,y) = arcsin(x^2+y^2-2)

    From what I've seen in an example problem arcsin(x^2+y^2-2) must be greater than 0 (not sure why this is) but I don't know for what values arcsin > 0 since it's a trig function that has positive and negative values...if someone could help, it would be greatly appreciated.
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    Quote Originally Posted by paulrb View Post
    Find the domain of the function
    f(x,y) = arcsin(x^2+y^2-2)

    From what I've seen in an example problem arcsin(x^2+y^2-2) must be greater than 0 (not sure why this is) but I don't know for what values arcsin > 0 since it's a trig function that has positive and negative values...if someone could help, it would be greatly appreciated.
    You require -1 \leq x^2 + y^2 - 2 \leq 1 \Rightarrow 1 \leq x^2 + y^2 \leq 3, which is the area between the circles x^2 + y^2 = 1 and x^2 + y^2 = 3
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