We can add and subtract multiples of 2 to or from the argument of the sine function without changing its value. The angle 2 corresponds to a whole turn in a unit circle and the sine function returns to the same value every time the angle changes by a complete revolution.
For example, if we can subtract sufficiently many 2's from 9, we will obtain a more manageable argument which lies between 0 and 2,
sin9=sin(9−2−2−2−2)=sin.
The line which makes an angle with the positive part of the x-axis is the negative part of the x-axis and it cuts the unit circle at the point (-1,0), which is why we can see from the y-coordinate that sin9=sin=0.
