There are four key points on the unit circle.
They are:
1) Two iintersections with the x-axis
2) Two intersections with the y-axis
Intersections with the x-axis
a) One of the point is 1 unit to the right of the origin (0,0). Then the intersections point is (1,0).
Those coordintatesidenfity the vector (1,0) whose angle is 0°.
And the trigonometric functions sin, cos, and tan are:
sin (0) = y-coordinate / radius of the circle = 0/1 =0
cos(0) = x-coordinate / radius = 1/1 =1
tan (0) = y-coordinate / x-coordinate = 0/1 = 0
b) The other intersection point with the x-axis is one unit to the left of the center => (-1,0), and agle = 180°
That drives to:
sin(180°) = y-coordinate / radius = 0/(-1) = 0
cos(180°) = x-coordinate / radius = -1/1 = -1
tan(180°) = y-coordinate / x-coordinate = 0 /(-1) = 0
Intersections with the y-axis
c) One point is 1 unit up of the center => coordinates are (0,1) and angle is 90°
Then,
sin (90°) = y-coordinate/radius = 1/1 = 1
cos(90°) = x-coordinate/ radius = 0/1 = 0
tan(90°) = y-coordinate/x-coordinate = 1/0 = undefined
d) The other intersection point with the y-axis is (-1,0), and the angle is 270°.
Then:
sin(270°) = y-coordinate / radius = -1/1 = -1
cos(270°) = x-coordinate / radius = 0/1 = 0
tan(270°) = y-coordinate / radius = -1/0 = undefined
