How many solutions does sin(x) = 0.01 have in the interval [0, 2p)?

Question

How many solutions does sin(x) = 0.01 have in the interval [0, 2π)?

My professor ran out of time before she could explain this, but what process would you take to solve this. Also how do you know if it falls in the interval?

wouldn't it be infinitely many?

Answer 1

The sine function is positive in QI and QII. Therefore sin(x) = 0.01 (or any other positive value) has only two solutions (within the interval [0, 2π).