If you wish to find the one unit circle equation, then make it sure your raduis where the point of origin at the center is 1;

by pytHAgEAN theorem; we have x^2 +y^2=c^2( hypotnuis)
 the hypo in a 1 unit circle equation, is equal to raduis;
raduis=1 unit:by PT;
c^2=raduis^2; where raduis is =1;
x^2 +y^2=1^2;
X^2+y^2=1...the importance of this equation in your farther discussion you will know the value of trig function (special case of a triangle) without using a calculator..