How many values of x satisfy the equation: sin⁡x=x^2/(625π^2 )?

Answer 1

Since sinx is always less than 1, you need to find where

x^2/625 >= 1

There will be no solutions past that. Looks like you don't need to look beyond x=25. So, how many periods does sinx have in that domain?

Looks like 4, positive and negative, so I expect there are 15 or 16 solutions. Check near x = ±25

Answer 2

34