In this discussion, you will discuss the relationships of key points on the unit circle. for the key points shown in the four quadrants on the unit circle, identify a significant pattern or symmetry in the angles, the coordinates, the trigonometric functions, or a relationship between them. post a detailed response to the discussion prompt.

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