I have recently had problems with the solutions proposed for trigonometric problems. For example, there is a case like 2 + 3cos *2x* = 0. For all trigonometric problems in any form, I know that I have to use algebra or trigonometric identities to isolate them *x* or theta or isolating a single trigonometric function with a single angle corresponding to a value on the right before finding all solutions. However, I am confused about the answers to many trigonometric problems. In the above example, it is limited to the range of *x* is less than or equal to 180 and greater than or equal to 0. Resolve for *x*I get -20.9 degrees. I see that this is out of range, but if I take the reflection amplitude of that answer (+0.36), I see that a line drawn in the graph of the Sin function intersects the function at two points one is +20.9 degrees and the other is 159.1 (180-20.9) degrees. But in my textbook it says that 110.9 degrees are the answer.

For this reason, I would appreciate any help that helps me understand how to find all solutions to a problem in a limited capacity. I have solved many of these trigonometric problems, but when I come to the point where I have to specify the solutions that will satisfy such problems, I am completely lost. I looked at several videos and read online tutorials on this topic in mathematics, but I can not see their reasons for multiple solutions.