How many real solutions does the inverse trigonometric equation sin⁻¹x = πx/2 have?

How many real solutions does the inverse trigonometric equation sin⁻¹x = πx/2 have?

• A. Zero
• B. One
• C. Exactly three
• D. Infinitely many

Answer: C) Exactly three

Explanation: Let f(x) = sin⁻¹x and g(x) = πx/2. Plotting both on their valid domain [−1, 1], they intersect at the origin (x = 0) and at the boundaries x = 1 (where both equal π/2) and x = −1 (where both equal −π/2). Thus, there are exactly three real solutions.