Find all the values of x, in between the range [0,2π] for the following equation. 2sin(3x)+3cos(3x)=0

Question

The equation is, 2sin(3x)+3cos(3x)=0.

Answer 1

sin 3x = -1.5 cos 3x

tan 3x = -1.5

Now just look up the values in the interval required in which tan=-1.5

Then divide those angles by 3 to get your answer.