please help me solve this equation: solve for x, 1 + 2sin(3x)=0, zero degrees is less than or equal to x and?

Question

x is less than 360 degrees. thanks so much!

Answer 1

2sin(3x)=-1
sin(3x)=-(1/2)
let 3x=u
for sin u=(-1/2), u=4(pi) / 3, 5(pi) / 3
so
x= 4(pi)/9, 5(pi)/9.

Answer 2

1+2sin(3x)=0
I will give you some hints:
hint 1: sin(3x)= -1/2

hint 2: subsitute 3x=y so you get sin(y)=-1/2, of course remember to change the interval too. If 3x=y and 0<=x<=360, what should the interval for y be?

Translate the values of y into x afterwards and you are done.

Answer 3

Solve the equation to get sin(3x) = -1/2; the angles for which sinø = -1/2 are π-π/6 and π+π/6 for 0≤ø≤2π. Then 3x= (5/6)π or (7/6)π and x = (5/18)π and x = (7/18)π