Solve for x the following 3cos(3x-1)=0.

First, we'll divide by 3 both
sides:

cos(3x-1)=0

Now, we'll
take the inverse function both sides. For this reason, since the cosine function is not
one to one function and inverse function can only be applied to one to one functions,
we'll restrict the domain of cosine function to [0;pi].

3x
- 1 = +/-arccos (0) + 2kpi, k is an integer number.

3x - 1=
+/- pi/2  + 2kpi

We'll add 1 both
sides:

3x = +/- pi/2  + 2kpi +
1

We'll divide by 3 to isolate
x:

x = +/- pi/6 +  2kpi/3 +
1/3

The solutions of the equation over the range [0;pi]
are:

x = pi/6 + 1/3