cos 3x = -cos 3x

Question

find all the solutions of the given equation in the interval 0≤x<2pi

Answer 1

what number is equal to its own negative? 0.

 

Okay, so if Cos(3x) = 0, then what possible values of 3x are there in the interval 0<=3x<=6pi that have that cosine?  There should be 2 such angles in each 2pi, so if we stretch it out to 6pi, there should be 6 solutions.  

 

For instance, if we were talking cos(3x) = .5, then 3x is pi/3 or 5pi/3 or 7pi/3 or 11pi/3 or 13pi/3 or 17pi/3, and x is 1/3 of each of those.  

 

So, what are the values for cos(3x) = 0?