Solve the equation for all solutions in the interval [0,2𝜋). cos(3𝑥)=−sqrt(3)/2 Express each solution in radians in exact form. Enter the solutions as a comma‑separated list.

Answer 1

The best way to approach this is to make a substitution of y =3x and solve for y

so cos y=-(sqroot 3)/2. So y = 150 degrees (5pi/6) and 210 degrees 7pi/6

since y=3x then 5pi/6=3x. X=5pi/18 and 7pi/6=3x x=7pi/18

the period of this function is 2pi/3 . if you add 5pi/18 +2pi/3 This equals 17pi/18 so this will be another solution between 0 and 2pi

So there are 3 solutions between 0-2pi ( 5pi/18, 7pi/18 and 17pi/18)