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

Solution:

If sin(x) = 0.01 then

Sin (x) = 1/100

The sine function is +ve in quadrant 1 and quadrant 2 and hence sin(x) = 0.01 will have two solutions i.e. 

x = sin^-1(0.01) and x = π - sin^-1(0.01) 

The figure below shows that why sin(x) = 0.01 has two values

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

Summary:

Sin(x) = 0.01 have two solutions in the interval [0, 2π)