If sin(3 theta)=-1 and 0</ theta <2pi, solve equation?

Question

solution is pi/2, 7pi/6, 11pi/6.
I know the period is 2pi but when does sin = -1?

Answer 1

sin(3x) = -1
then 3x can be
3x = 3pi/2,5pi/2, 7pi/2, 9pi/2 , 11pi/2, 13pi/2 and so on,
there fore
x = 3pi/6, 5pi/6, 7pi/6, 9pi/6, 11pi/6, 13pi/6 and so on
but solution
only 3pi/6, 5pi/6, 7pi/6, 9pi/6, 11pi/6 will be in the given range.

Answer 2

sin(3@)=-1 means 3@= 3pi/2 +2kpi k an integer

@= pi/2 +2kpi/3

Giving k =0 @=pi/2, k= 1 @= pi/2+2pi/3 =7pi/6,k=2 @=pi/2+4pi/3 = 11pi/6. The next is outside the intervall and is the first plus the period 2pi

Answer 3

Theta = 90 degrees
Sin is at negative one at 270 degrees, divided by 3 equals 90 degrees.
Or as you put it pi/2.