Question

Solve sin(3x)cos(8x) - cos(3x) * sin(8x) = - 0.65 for the smallest positive solution

Answer 1

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