Question

Why does a calculator return an error when trying to find inverse sine of 1.055?

Answer 1

Sin(x) is a function bounded between -1 and 1. A value greater than 1 or smaller than -1 (-1.1, for instance) does not correspond to any real angle.

It then returns error

Answer 2

1.055 is outside the domain of the sine function.

Explanation:

When we are taking the inverse sine, we are finding an angle that gives a value of 1.055.

The sine function NEVER gives a value greater than 1 or less than -1. The domain of the sine function is between -1 and 1, inclusive.

So wanting to know which angle gives a sine value of 1.055 is futile. Sine can never be greater than 1.

That's why the calculator gives an error, because 1.055 is outside the domain of the sine function.