Algebra & Trig, Sullivan & Sullivan
Fourth Edition
Notes:§6.7
Page 1 / 3
§6.7 – Graphing The Other Trig Functions
Having graphed the (co)sine functions, we're now going to go on to (co)tan, and (co)secant.
We'll use the same basic approach as we did for (co)sine
Let's look at Tan,
Cot, on the unit circle:
Sin
Cos
Tan = Sin/Cos
Cot = Cos/Sin
Sin 0° = 0
Cos 0° = 1
Tan 0° = 0
Undefined
Sin 30° =
Sin 45° =
1
2
1
Cos 30° =
Cos 45° =
2
2
1
Cos 60° =
2
3
2
Sin 60° =
Sin 90° = 1
Cos 90° = 0
3
2
1
Sin 60° =
Sin 45° =
Cos 45° =

Sin 240° = 
1
2
1
2
3
2
Sin 270° = -1 (
Sin 300° = 
Sin 315° =

3
2
1
2
1
Sin 330° = 
2
Sin 360° = 0
2
3
2
Cos 30° = 
Sin 180° = 0
Sin 225° =

Tan 30° =
1
3
3
=
3
3
Tan 45° = 1
1
1
3
Tan 60° =
=
3
Cos 180° =-1
Cos 210° =
3

2
Tan 120° = Tan 60° =

 3
Tan 135° = Tan 45° =
Tan 150° =Tan30°= 
1
= 
3
=
3
3
= 
3
3
-1
3
3
 3
Tan 180° = 0
Tan 210° =
1
-1
1
3
3
0
Tan 90° = Undefined
1
2
1
Cos 60° = 
2
1
Sin 30° =
2
Sin 210° = 
3
2
1
Undefined
3
3
3
Cos 225° =

1
Tan 225° = 1
1
2
Cos 240° = 
1
2
Cos 270° = 0
Cos 300° =
Cos 315° =
1
2
1
2
Cos 330° =
3
2
Cos 360° = 1
Tan 240° =
1
3
=
3
0
Tan 270° = Undefined
Tan 300° =

1
3
= 
3
3
 3
Tan 315° = -1
Tan 330° =
 3
Tan 360° = 0
3
3
-1

1
3
= 
3
3
Undefined
Algebra & Trig, Sullivan & Sullivan
Fourth Edition
Notes:§6.7
Page 2 / 3
As a result, the tan function looks like:
(Thanks to library.thinkquest.org/ 20991/alg2/trig.html for the image!)
Cot looks like:
(Thanks to http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Umberger/EMAT6690smu/Day5/Day5.html )
Algebra & Trig, Sullivan & Sullivan
Fourth Edition
Notes:§6.7
Cosecant (the reciprocal of sine)
Similarly, the secant line: (the reciprocal of cosine)
(both are thanks to http://home.alltel.net/okrebs/page74.html )
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