Final answer:
The expression arcsin(−√2) is undefined because the value −√2 is outside the domain of the arcsin function, which is −1 to 1.
Step-by-step explanation:
The student has asked to evaluate the expression arcsin(−√2). The arcsin function, also known as the inverse sine, gives us the angle whose sine is the number provided.
However, the question contains an error because the sine function for a real angle in trigonometry will always give a result within the range of −1 to 1. Since −√2 is less than −1, this is not within the domain of the arcsin function, meaning the expression arcsin(−√2) is undefined.
In general, for a real number x, arcsin(x) is only defined for −1 ≤ x ≤ 1. For values outside this range, the expression is not valid in real numbers.