To solve the equation 2 sin(x) + 1 = 0, isolate the sin(x) term and determine the angles where sin(x) equals the given value. The solutions for x are 210 degrees and 330 degrees, or 7π/6 and 11π/6 in radians.
Given the equation 2 sin(x) + 1 = 0, we want to solve for x. To do this, we'll isolate the sin(x) term by subtracting 1 from both sides, resulting in 2 sin(x) = -1. Next, divide both sides of the equation by 2 to get sin(x) = -1/2.
We know that the sine function takes on specific values at certain angles. Using the unit circle, we can find the angle(s) where sin(x) = -1/2.
In the first quadrant, sin(x) = 1/2. In the second and third quadrants, sin(x) is negative.
Therefore, the solutions for x are x = 210 degrees and x = 330 degrees.These solutions can also be written as x = 7π/6 and x = 11π/6 in radians.