When two trigonometric graphs such as sine and cosine intersect, we call that point of intersection a solution of the system of equations. This is the same meaning that solutions of systems of linear equations has.
Solutions of Systems of Sine and Cosine graphs
![Picture of graph of system of sine and cosine equations](images/picture-system-sinex-cosx.gif)
As you can see from the graph, this system of sine and cosine graphs intersect twice during this interval. They intercept at x = Π/4 as well as at x = 5Π/4
![](images/system-of-trigonometric-equations2-no-solution.gif)
![](images/graph-system-of-sin2x-and-cosx.gif)