1. The Unit Circle

2. Warm-up 1 2 3 4 5 6

3. The hypotenuse for each triangle is 1 unit.
sin
The x-axis: cosine function
The y-axis: sine function. 1
cos
In order to create the unit circle, we must use the special right triangles below:
45º 1
60º 1
30º
45º
30º 60º 90º
45º 45º 90º
The hypotenuse for each triangle is 1 unit.

4. You first need to find the lengths of the other sides of each right triangle...
45º 1 1
60º
30º
45º

5. Now, use the corresponding triangle to find the coordinates on the unit circle...
(0, 1)
sin
What are the
coordinates of
this point?
This cooresponds
to (cos 30,sin 30)
(Use your
triangle)
(cos 30, sin 30)
30º
cos
(1, 0)
(–1, 0)
(0, –1)

6. Now, use the corresponding triangle to find the coordinates on the unit circle...
(0, 1)
sin
What are the
coordinates of
this point?
(Use your
triangle)
(cos45, sin 45)
(cos 30, sin 30)
45º
cos
(1, 0)
(–1, 0)
(0, –1)

7. You can use your special right triangles to find any of the points on the unit circle...
(0, 1)
sin
(cos45, sin 45)
(cos 30, sin 30)
cos
(1, 0)
(–1, 0)
(Use your
triangle)
What are the
coordinates of
this point?
(0, –1)
(cos 270, sin 270)

8. Use this same technique to complete the unit circle on your own.
(0, 1)
sin
(cos45, sin 45)
(cos 30, sin 30)
cos
(1, 0)
(–1, 0)
(0, –1)
(cos 270, sin 270)