1st Question) Cos 3x = - 1/sqrt(2) 2nd question) Sin(cos(5x))=0

Question

For the 1st question, I had find all solutions of the equation which is pi/4 + 2pi/k, x= 5pi/12 + 2pi.k/3. Although you can double check if it's correct. The problem I'm having is that I have to find all the solutions in the [0,2pi] Interval. I hope you can explain in detail with steps.

For the 2nd question, I don't know how to find it, please help me.

Answer 1

The best way to attack these questions is to graph the equations first.

The first one 3x = arc cos (-.5 sqrt(2)).

The second one will be done in essentially the same way.

And the graph will show you what quadrants you need.