Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) sin(cos−1( sqrt 3 ))

Question

sin(cos^-1(√3))

Answer 1

cos^-1(√3) or arccos(√3) means, "what angle results in a cosine of √3"? Positive values of cosine are found in Q1 and Q4 but arccos has ranges only in Q1 and Q2 therefore we MUST be in Q1. HOWEVER, √3 is a number approx equal to 1.7 and cosine of any angle only results in numbers between -1 and 1 therefore, there are NO angles that give us values of 1.7 making this impossible.