Question
Find the number of real solutions of sinx=x
Solution
We are given the equation: sin(x) = x We are to find how many real solutions this equation has. We are comparing two functions:
- f₁(x) = sin(x) — bounded between [–1, 1], periodic, continuous
- f₂(x) = x — an unbounded straight line
- At x = 0: sin(0) = 0 ⇒ x = 0 is a solution
- For x ≠ 0:
- For x in (0, 1]: sin(x) < x
- For x in [–1, 0): sin(x) > x
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