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

Question

Please do it in step by step..I got stuck in this math..It's urgent.

Answer 1

2sin(3x) + 3cos(3x) = 0

2sin(3x) = -3cos(3x)

sin(3x)/cos(3x) = -3/2

tan(3x) = -3/2

3x = tan^-1(-3/2)

x = (1/3) tan^-1(-3/2)

Use your calculator to find tan^-1(-3/2). It will give you a negative angle value, which is not in the range 0 to 2π ( 0 to 360°). The tangent function repeats every 180°, so just keep adding 180 to the value from the calculator to find the values for x in the interval 0 to 360°.