EquationMediumQuestion 200053
Question
The equation sin x = x/100 has approximately how many solutions in (−∞, ∞)?
- A101
- B63Correct
- C31
- Dinfinite
Correct answer
63
Explanation
sin x oscillates between −1 and 1. The line y = x/100 intersects the sine curve when −1 ≤ x/100 ≤ 1 → −100 ≤ x ≤ 100. In this range, there are about 100/(π) ≈ 31.8 cycles. Each full cycle gives 2 crossings (going up and down). Approximately 2 × 100/π + 1 ≈ 63 solutions.