Math Help - Find Exact solution over the interval [0.2pi)

1. Find Exact solution over the interval [0.2pi)

I need to get the exact solutions over the interval [0,2pi)

Sin 3x= -1

I have the intervals 0< x < 2pi

I am having trouble getting the first set of numbers with this inequality.
I have that the angle is 30 degrees of pi/6.

And the answer book says i should get

pi/6, 7pi/6, 13pi/6, 19pi/6, 25pi/6, and 31pi/6

I can get 4 of these by adding 2pi to each one, but i can't get 7pi/6 or 25pi/6.

Can anyone help? Thanks!

2. Originally Posted by KoolFlair
I need to get the exact solutions over the interval [0,2pi)

Sin 3x= -1

I have the intervals 0< x < 2pi

I am having trouble getting the first set of numbers with this inequality.
I have that the angle is 30 degrees of pi/6.

And the answer book says i should get

pi/6, 7pi/6, 13pi/6, 19pi/6, 25pi/6, and 31pi/6

I can get 4 of these by adding 2pi to each one, but i can't get 7pi/6 or 25pi/6.

Can anyone help? Thanks!
I disagree with the book's solution.

$0 \le x < 2\pi$

$0 \le 3x < 6\pi$

$\sin(3x) = -1$

$3x = \frac{3\pi}{2} \, , \, \frac{7\pi}{2} \, , \, \frac{11\pi}{2}$

$x = \frac{\pi}{2} \, , \, \frac{7\pi}{6} \, , \, \frac{11\pi}{6}$