The expression sin^-1(4/5) has an infinite number of values? true or false

Question

The expression sin^-1(4/5) has an infinite number of values?

A. True

B. False

Answer 1

Tricky! Yes, there are an infinite number of angles for which sin(θ) = 4/5. However, the inverse sine function has a limited domain [-1, 1] and range [-90°, 90°], meaning that there is only one answer (≈53°) for sin^-1(4/5). To make a parallel example, the equation x² = 9 has two solutions: x = ±3... and yet the equation x = √9 has only one solution x = 3. This is because the domain and range of the square root function (inverse of square function) are limited. Does that make sense? Long story short, the answer is FALSE :)