Section 6.1 Notes

Special Angles of the Unit Circle

in degrees and radians

What are the special right

triangles?

45 45 90

30 60 90

The same angles that form the angles

of special right triangles are the

special angles of the unit circle.

Let’s take a look at those beginning

with the multiples of 90o angles, also

called the quadrantal angles.

quadrantal

0 , 0

360 , 2

180 ,

3270 ,

2

90 ,2

Multiples of 45o

45180 4

Multiples of 45o

45 2 90 , 24 2

345 3 135 , 3

4 4

45 4 180 , 44

Multiples of 45o

545 5 225 , 5

4 43

45 6 270 , 64 2

745 7 315 , 7

4 4

45 8 360 , 8 24

multiples of 45o

7315 ,

4

3135 ,

4

5225 ,

4

45 ,4

Multiples of 60o

60180 3

Multiples of 60o

260 2 120 , 2

3 3

60 3 180 , 33

460 4 240 , 4

3 3

Multiples of 60o

560 5 300 , 5

3 3

60 6 360 , 6 23

multiples of 60o

5300 ,

3

2120 ,

3

4240 ,

3

60 ,3

Multiples of 30o

30180 6

Multiples of 30o

30 2 60 , 26 3

30 3 90 , 36 2

230 4 120 , 4

6 3

Multiples of 30o

530 5 150 , 5

6 6

30 6 180 , 66

730 7 210 , 7

6 64

30 8 240 , 86 3

Multiples of 30o

330 9 270 , 9

6 25

30 10 300 , 106 3

1130 11 330 , 11

6 6

30 12 360 , 12 26

multiples of 30o

11330 ,

6

5150 ,

6

7210 ,

6

30 ,6

Now let’s take a look at the entire

unit circle in degrees...

3045

6090120

150

0180

330315

300270

240225

210

135

,360

Now let’s take a look at the entire

unit circle in radians...

special angles - radians

6

4

3

0

2

2

3

3

4

5

6

7

6

5

4

4

3

3

2

11

6

7

4

5

3

, 2

?45 :

4?

30 :6

?60 :

3

multiples

multiples

multiples