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, iden
Mathematics
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Question
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.
1 Answer

1. User Answers Edufirst
There are four key points on the unit circle.
They are:
1) Two iintersections with the xaxis
2) Two intersections with the yaxis
Intersections with the xaxis
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) = ycoordinate / radius of the circle = 0/1 =0
cos(0) = xcoordinate / radius = 1/1 =1
tan (0) = ycoordinate / xcoordinate = 0/1 = 0
b) The other intersection point with the xaxis is one unit to the left of the center => (1,0), and agle = 180°
That drives to:
sin(180°) = ycoordinate / radius = 0/(1) = 0
cos(180°) = xcoordinate / radius = 1/1 = 1
tan(180°) = ycoordinate / xcoordinate = 0 /(1) = 0
Intersections with the yaxis
c) One point is 1 unit up of the center => coordinates are (0,1) and angle is 90°
Then,
sin (90°) = ycoordinate/radius = 1/1 = 1
cos(90°) = xcoordinate/ radius = 0/1 = 0
tan(90°) = ycoordinate/xcoordinate = 1/0 = undefined
d) The other intersection point with the yaxis is (1,0), and the angle is 270°.
Then:
sin(270°) = ycoordinate / radius = 1/1 = 1
cos(270°) = xcoordinate / radius = 0/1 = 0
tan(270°) = ycoordinate / radius = 1/0 = undefined