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Any books we've used throughout high school and university preferred the '^-1' notation, leading me to believe that the 'arc-' notation is archaic. It feels like we're taught it, but discouraged from using it (similar to the situation between Imperial and SI units).

Is this true? If not, then is this notation more widespread outside of Canada and the States?

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    Here in Sweden it's almost always "arc".2012-09-20

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I don't know if there's a general trend. I've always preferred the "arc" terminology, as there's less chance of confusion between the inverse function and the reciprocal. It's certainly not "archaic".

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Here in France, the notation has also changed in the same way. Maybe it's due to pocket calculators. cos^-1 is shorter...