Answer:
0.24+n*pi and 1.33+n*pi
Step-by-step explanation:
First you add three to both sides to get:
13sin(2x)=6
Then you divide by thirteen to both sides to get:
sin(2x)= 6/13
Next, you use a calculator to perform the inverse of sine to both sides, which is arcsin, and cancels out the sin.
arcsin(sin(2x))= arcsin(6/13) -> 2x= arcsin(6/13)
Arcsin(6/13)= approximately 0.48. But besides 0.48, there is another solution, because the y value of 6/13 can have two possible x values, both in quadrant one and two. We found the quadrant one value. The quadrant two value is just pi-0.48=2.66.
So, if we add two pi (360 degrees) to both of these solutions for n amount of times, then on a graph, we would end up on the same point every time. Each of those revolutions around the graph is one solution. These are the solutions:
2x= 0.48+n*2pi -> 0.24+n*pi
2x=2.66+n*2pi -> 1.33+n*pi
