Solving trig equations | Negative Ratio

In this example problem, we solve a trigonometric equation by isolating the trig function on one side by itself and a ratio on the other side. A side equation is set up that looks less difficult and involves the basic variable of y. We solve this side equation for our variable and then use the same steps to solve our given equation for sin(*). After our trig function is isolated, we find that it equals a negative ratio (fraction). The ratio is one that occurs often with nice angles, so we identify the angle that when evaluated in the function will produce the positive version of the ratio. That angle is then used as a reference angle in other quadrants to find angles that will be negative for our sine function. Each part of this process is explained and written out step-by-step.

2sin(*)+1=0
2sin(x)+1=0