A sine wave repeats every 360 degrees. So why does sin(x) = sin(180-x)? Shouldn't that be sin(x) = sin(360-x)? Also, is there an equation that shows how sin(x) = sin(90+(90-x))? I'm talking about the symmetry around quarters, such that sin(80) = sin(100) because they're equally different from 90. However, while this pattern repeats around the 90 and 270 point, around the 180 point sin(170) = -1*(sin(190)). Is there a single equation that accounts for all this?