Question

Explain why the the inverse of sine times 1.5 does not make sense.

Answer 1

This doesn't make sense, because the the sin of any number never has a value greater than 1. This is because the inverse of sin (or arcsin, if you will) of a value (like 1.5, in this example) asks for what value of theta (what angle measure on the unit circle) the sin will be equal to that value (1.5). Because the sin of any angle is never greater than one, one cannot take the arcsin of any value greater than 1.