Unit Circle
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Angles and Radians of a Unit Circle Positive: sin, csc Negative: cos, tan, sec, cot
(0,1)
tan 90! = undefined
2π / 3
(
3π / 4
(−
3 / 2, 1/ 2
90
(1/ 2,
!
120!
( −, + )
3/2
( +, + )
)
(
!
2 / 2, 2 / 2
π /6
150!
II
tan 60! = 3
π /4
60! 45
)
π
(-1,0)
(
30!
I
180!
3 / 2, 1/ 2
)
tan 30 = !
0! 2π 360!
tan 0! = 0
)
tan 45! = 1
3 3
(1,0)
III IV
7π / 6
(−
)
π /3
π /2
)
135!
5π / 6
(−
−1/ 2, 3 / 2
2 / 2, 2 / 2
Positive: sin, cos, tan, csc, sec, tan Negative: none
!
3 / 2, − 1/ 2 5π / 4
(−
)
210
( −, − ) ( + , − )
225!
)
2 / 2, − 2 / 2 4π / 3
240!
(−1/ 2, −
!
270 3/2
Positive: tan, cot Negative: sin, cos, csc, sec
Courtesy of Randal Holt. Original Source Unknown. http://www.MathematicsHelpCentral.com
3π 2
3 / 2, − 1/ 2
7π / 4
300!
(1/ 2, − (0,-1)
(
315!
5π / 3
)
11π / 6
330!
(
2 / 2, − 2 / 2
3/2
)
Positive: cos, sec Negative: tan, cot, sin, csc
)
)
(0,1)
tan 90! = undefined
2π / 3
(
3π / 4
(−
3 / 2, 1/ 2
90
(1/ 2,
!
120!
( −, + )
3/2
( +, + )
)
(
!
2 / 2, 2 / 2
π /6
150!
II
tan 60! = 3
π /4
60! 45
)
π
(-1,0)
(
30!
I
180!
3 / 2, 1/ 2
)
tan 30 = !
0! 2π 360!
tan 0! = 0
)
tan 45! = 1
3 3
(1,0)
III IV
7π / 6
(−
)
π /3
π /2
)
135!
5π / 6
(−
−1/ 2, 3 / 2
2 / 2, 2 / 2
Positive: sin, cos, tan, csc, sec, tan Negative: none
!
3 / 2, − 1/ 2 5π / 4
(−
)
210
( −, − ) ( + , − )
225!
)
2 / 2, − 2 / 2 4π / 3
240!
(−1/ 2, −
!
270 3/2
Positive: tan, cot Negative: sin, cos, csc, sec
Courtesy of Randal Holt. Original Source Unknown. http://www.MathematicsHelpCentral.com
3π 2
3 / 2, − 1/ 2
7π / 4
300!
(1/ 2, − (0,-1)
(
315!
5π / 3
)
11π / 6
330!
(
2 / 2, − 2 / 2
3/2
)
Positive: cos, sec Negative: tan, cot, sin, csc
)
)
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