GATE 2016 EC (EC2) – Question 14
How many distinct values of $x$ satisfy $\sin x=x/2$, where $x$ is in radians?
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (C) 3
Explanation
Since $|\sin x|\le1$, every solution has $|x|\le2$. Zero is one solution and the equation is odd, so nonzero roots occur in opposite pairs.
On (0,2), $\sin x-x/2$ is strictly concave, initially increasing from zero and negative at x=2. It crosses zero exactly once there, near 1.8955. Its negative is the other root. Thus there are **three roots, C**.