How to formulate this type of arcsin problem?

Question

Reading and commenting on What are some common ways students get confused about finding an inverse of a function? I was kindly set straight that the use of $\sin^{^{-1}}(x)$ to mean $\arcsin(x)$ has been rendered obsolete. International Standard ISO 80000-2 offers the following:

This notation is preferable to me, with one point of confusion. The text we use, Algebra and Trigonometry by Paul Foerster, uses $\textrm{Arcsin}(x)$ to indicate the restricted domain, and the lower case as above for all real domain. This notation leaves me with my question -

How do we ask for the arcfunction with no domain restriction, i.e we actually want the multiple answer as in "solve for the first 6 values when $y=2$ for the following sinusoidal function" ?

Disclosure - This question is in reaction to my discovering that a notation that I never cared for has been eliminated by an international standard for nearly 10 years, but still used at my high school. I am trying to understand where to go with this as people in general aren't so open to change.

Answer 1

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