section 6.1 notes special angles of the unit circle in degrees and radians
TRANSCRIPT
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Section 6.1 Notes
Special Angles of the Unit Circle
in degrees and radians
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What are the special right
triangles?
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45 45 90
30 60 90
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The same angles that form the angles
of special right triangles are the
special angles of the unit circle.
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Let’s take a look at those beginning
with the multiples of 90o angles, also
called the quadrantal angles.
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quadrantal
0 , 0
360 , 2
180 ,
3270 ,
2
90 ,2
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Multiples of 45o
45180 4
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Multiples of 45o
45 2 90 , 24 2
345 3 135 , 3
4 4
45 4 180 , 44
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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
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multiples of 45o
7315 ,
4
3135 ,
4
5225 ,
4
45 ,4
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Multiples of 60o
60180 3
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Multiples of 60o
260 2 120 , 2
3 3
60 3 180 , 33
460 4 240 , 4
3 3
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Multiples of 60o
560 5 300 , 5
3 3
60 6 360 , 6 23
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multiples of 60o
5300 ,
3
2120 ,
3
4240 ,
3
60 ,3
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Multiples of 30o
30180 6
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Multiples of 30o
30 2 60 , 26 3
30 3 90 , 36 2
230 4 120 , 4
6 3
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Multiples of 30o
530 5 150 , 5
6 6
30 6 180 , 66
730 7 210 , 7
6 64
30 8 240 , 86 3
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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
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multiples of 30o
11330 ,
6
5150 ,
6
7210 ,
6
30 ,6
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Now let’s take a look at the entire
unit circle in degrees...
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3045
6090120
150
0180
330315
300270
240225
210
135
,360
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Now let’s take a look at the entire
unit circle in radians...
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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
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?45 :
4?
30 :6
?60 :
3
multiples
multiples
multiples