what are all the solutions rounded to four decimal places? ANSWERS ONLY

Question

Find all solutions on [0, 2π).

 (Enter your answers as a comma-separated list. Round your answers to four decimal places.)

10 sin²(x) + 7 sin(x) + 1 = 0

Answer 1

sin0=0

sin360=0

Answer 2

Even though you said "answers only", no good tutor would just give you the answers. I will give you the shortest explanation I can come up with.

First, let w = sin(x). Our equation becomes:

10w² + 7w + 1 = 0

Use any method you want to solve the quadratic (i.e factoring, quadratic formula, etc) to obtain the following results:

w = -1/2

w = -1/5

Substitute w = sin(x) back into the solutions above to get:

sin(x) = -1/2

sin(x) = -1/5

If we apply arcsin(x) to both sides of both equations, we get:

x = 7π/6, 11π/6

x = 6.08 radians, 3.34 radians