Each real number t corresponds to a point (x, y) on the .
To do so, let's consider the unit circle that is given by the equation x^2+y^2=1.
Let's imagine that the real number line is wrapped around this circle, with positive numbers corresponding to a counterclockwise wrapping and negative numbers corresponding to a clockwise wrapping.
As the real number line is wrapped around the unit circle, each real number t corresponds to a point (x,y) on the unit circle. For example, the real number 0 corresponds to the point (1, 0). In addition, because the unit circle has a circumference of 2Ï€, the real number 2Ï€ also corresponds to the point (1, 0).
In general, each real number t also corresponds to a central angle in standard position. If the real number t corresponds to a point (x,y) on the unit circle, then (x, y) is point of intersection of the unit circle and the terminal side of the angle in standard position with the measure of t.
Now we can complete the sentence.
Each real number t corresponds to a point (x, y) on the unit circle.
