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Let’s think back to Geometry…
…and the special right triangles
a a
a30
6045
3a a2 2a
Now, let’s apply it to the unit circle…
What does “unit circle” really mean?
It’s a circle with a radius of 1 unit.
What is the equation of the “unit circle”?
122 yx
, 180 0, 02, 360
3
2
2
1,0
0,1
-1,0
0, -1
, 180 0, 02, 360
3
2
2
Let’s begin with an easy family…4
2
2
2
2
1
45
2
2,
2
2
What are the coordinates?
4
Now, reflect the triangle to the second quadrant…
What are the coordinates?
, 180 0, 02, 360
3
2
2
2
2
2
2
1
45
2
2,
2
2
4
Now, reflect the triangle to the third quadrant…
1
-2
2
2
2
-2
2,
2
2 3
4
What are the coordinates?
Now, reflect the triangle to the fourth quadrant…
, 180 0, 02, 360
3
2
2
2
2
2
2
1
45
2
2,
2
2
4
1
-2
2
2
2
-2
2,
2
2 3
4
-2
2, -
2
2 5
4
What are the coordinates?
, 180 0, 02, 360
3
2
2
2
2
2
2
1
45
2
2,
2
2
4
1
-2
2
2
2
-2
2,
2
2 3
4
-2
2, -
2
2 5
42
2, -
2
2 7
4
30
1 1
2
3
2
6
3
2,1
2
Now, reflect the triangle to the second quadrant.
30
1 1
2
3
2
6
3
2,1
2
Now, reflect the triangle to the third quadrant.
5
6
1
2
-3
2
-3
2,1
2
30
1 1
2
3
2
6
3
2,1
2
Now, reflect the triangle to the fourth quadrant.
5
6
1
2
-3
2
-3
2,1
2
-3
2, -
1
2
What are the coordinates? 7
6
What are the coordinates?
30
1 1
2
3
2
6
3
2,1
2 5
6
1
2
-3
2
-3
2,1
2
-3
2, -
1
2 7
6
3
2, -
1
2
11
6
Let’s look at another “family”3
1
, 180 0, 02, 360
3
2
2
60
3
2
1
2
1
2,
3
2
3
Now, reflect the triangle to the second quadrant
1
, 180 0, 02, 360
3
2
2
60
3
2
1
2
1
2,
3
2
3
Now, reflect the triangle to the third quadrant
13
2
-1
2
What are the coordinates?
-1
2,
3
2 2
3
Now, reflect the triangle to the fourth quadrant
1
, 180 0, 02, 360
3
2
2
60
3
2
1
2
1
2,
3
2
3
13
2
-1
2
-1
2,
3
2 2
3
What are the coordinates?
-1
2, -
3
2 4
3
1
, 180 0, 02, 360
3
2
2
60
3
2
1
2
1
2,
3
2
3
13
2
-1
2
-1
2,
3
2 2
3
-1
2, -
3
2 4
3
1
2, -
3
2
What are the coordinates?
5
3
