Look at the values of y in the range 0<x<pi and then look at its values in the range pi<x<2pi, can you see that they're exactly the same values except the latter are negative?
Look at the values of y in the range 0<x<pi and then look at its values in the range pi<x<2pi, can you see that they're exactly the same values except the latter are negative?
So if you take any of the x values from that first range and add pi to it, the resulting y value will be the same as it was originally, just negative. It's all to do with the periodicity of the function.
So if you take any of the x values from that first range and add pi to it, the resulting y value will be the same as it was originally, just negative. It's all to do with the periodicity of the function.
Note that the graph isn't the reason for the relationship - the graph is a consequence of the relationship!
If you want to understand WHY it's true, think about the definition of cos and sin as the x and y coordinates of a point moving round the unit circle. What happens to the y coordinate (sin) if you start with a point in the first quadrant and add pi radians to its angle (i.e. the angle the radius vector makes with the positive x axis)?