# Help finding the domain of a multivariable function

• Nov 10th 2008, 08:01 PM
paulrb
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.
• Nov 10th 2008, 08:27 PM
mr fantastic
Quote:

Originally Posted by paulrb
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 $x^2 + y^2 = 3$