Hello, I am doing trigonometry, and would appreciate a quick answer check. I'll explain what is throwing me off after.

Solve 6sin^2x+sinx-1=0 to nearest hundredth of a radian for (0, 2pi).

Let k=sinx

6k^2+k-1=0

(2k+1)(3k-1) or

(2sinx+1)(3sinx-1)

2sinx+1=0

sinx=(-1/2)

Focus angle is sinx=(1/2) = (pi/6)

Since sinx is negative, find the angle in quadrants three and four.

pi + (pi/6) = 7(pi)/6 and 2pi - (pi/6) = 11(pi)/6

So,

7(pi)/6

11(pi)/6

3sinx-1=0

sinx=(1/3)

Focus angle is sinx=(1/3)

Since sinx is positive, find the angle in quadrants one and two.

x=sin^-1(1/3)

x=19.47 or 19.47(pi)/180 = 0.34 r

(pi)-(19.47(pi)/180) = 160.53(pi)/180 = 2.80 r

So my final answer:

11(pi)/6 OR 5.76r

7(pi)/6 OR 3.67r

19.47(pi)/180 OR 0.34r

160.53(pi)/180 OR 2.80r

Now the thing that confuses me is, we know that this is a wave, and we are finding all points on the wave for x when y=0 (x-intercepts). If this is true, would there not be a common difference between two of the values for x? Or does this only apply when the wave has the point of origin as one of its x-values?

Thanks for the help again, and sorry I'm not using proper notation, I'm new to these boards.