Find all solutions to the following equation: 2 sin x + 1 = 0 2 sin x + 1 = 0?

2 sin x + 1 = 0

2 sin x = -1

sin x = -0.5

Now arcsin (0.5) = pi/6

Since sin x is negative, the angle x is in the third or fourth quadrant, for one complete revolution.

That is, x = pi + pi/6 = 7pi/6

Or x = 2pi - pi/6 = 11pi/6

For all revolutions, all of the solutions are given by adding 2n pi, since 2pi is one complete revolution.

So answer is C.

2sin(x) + 1 = 0

2sin(x) = -1

sin(x) = -½

x = 1.5πk ± π/3, where k is an integer