So,
For this problem, we could use the following trigonometric identity:
In this problem, we're given the expression:
Using the identity, the last equation is exactly the same as the next one:
Now, we could solve the equation:
As you can see in the image above, there are two angles in the interval [0,pi) such that the sin function equals 0.65. So, there are two solutions. We're going to add up 2kpi/5 which represents the period, with k as an integer number.
We're asked to find the smallest positive solution. That's when k=0. So, the answer is about x=0.14
