(a) The unit circle is the circle centered at (0,0) with radius 1.
(b) The equation of the unit circle is x^2 + y^2 = 1.
(c) Suppose the point P(x,y) is on the unit circle. Find the missing coordinate:
(i) P(1,√0)
(ii) P(√0,1)
(iii) P(-1,√0)
(iv) P(√0,-1)
(a) If we mark off a distance t along the unit circle, starting at (1,0) and moving in a counterclockwise direction, we arrive at the point (cos(t), sin(t)).
(b) The terminal points determined by π/2, π, -π/2, 2π are (0,1), (-1,0), (0,-1), (1,0) respectively.
If the terminal point determined by t is P(a,b), then the terminal point determined by t+2π is P(a,b).
The terminal point for t=π/3 is (1/2, √3/2) and so the terminal point for t=7π/3 is (-1/2, -√3/2).