To locate we reason as follows. Let P (t) be the ordered
pair P(x,y). For every value of 't' the point P(t) is on the unit circle. Therefore, if one of
the coordinates of P(t) is known, using x ^{2} + y^{2} = 1, we can find the other coordinate (except
for sign).
From the plane geometry, P is the midpoint of arc AA' which is equidistant from
x
and y axes so that x = y (see fig. no. 3)
Construct PM perpendicular to OA. Then, from school geometry OM= 1/2 OA but OA = 1.
Therefore OM = (See fig. no. 4)
Hence x = using x^{2} + y^{2} = 1
(1/2)^{2} + y^{2}= 1
The coordinates of and so on, can be obtained without too much difficulty.
