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
Pictured below is a system made up of the equation y = sin(x) and y = cos(x) over the interval 0≤X≤2Π
Solutions of the system
As you can see from the graph, this system of sine and cosine graphs interesect twice during this interval. They intercept at x = Π/4 as well as at x = 5Π/4
Can you figure out how many, if any, solutions there are for the following system of trigonometric equations has any solutions over the interval 0≤X≤2Π
The system of equations
y = sin(x) − 1
y = cos(x) + 1
Solutions of the system
Can you figure out how many, if any, solutions there are for the following system of trigonometric equations has any solutions over the interval 0 ≤ X ≤ Π
