# Math 140 Trigonometry 2.6: Graphing the Six Trigonometric

```Math 140
2.6: Graphing the Six Trigonometric Functions on your Calculator
Trigonometry
When graphing the six trigonometric functions instead of using Standard Zoom (ZOOM  6: ZStandard) we
use Trigonometric Zoom (ZOOM  7: ZTrig). See below.
Trigonometric Zoom resets the viewing rectangle so that it goes from [–2  , +2  ] along the x–axis with a tick mark
every  /2 radians. In other words there is a marker every  /2 radians along the x–axis. So counting from left to
right along the x–axis we have markers at –2  , –3  /2, –  , –  /2, 0,  /2,  , 3  /2, and 2  . For x = ±2  the
markers do not show because they are up against the left and right edges of the viewing rectangle. Also, the y–axis
goes from [–4, +4] with a tick mark every 1 unit. (Note: 6.1522856  2  and 1.5707963   /2)
Sine: y = sin x
Cosine: y = cos x
Tangent: y = tan x
Cosecant: y = csc x
Secant: y = sec x
Cotangent: y = cot x
BASIC Facts about the Six Trigonometric Functions
Domain
(–, +)
(–, +)
Range
[–1, +1]
[–1, +1]
Period
2
2
Even/Odd
Odd
Even
 k
2
, x  k
(–, +)

Odd
(–, –1]  [+1, +)
2
Odd
Sine
Cosine
Tangent
Cosecant
Secant
Cotangent
, x 


 k
2
(–, –1]  [+1, +)
2

, x  k
(–, +)
Where k is an integer, k = … , –3, –2, –1, 0, 1, 2, 3, …
, x 
Even
Odd
Note that in set builder notation:
o A domain or range of “all real numbers” is never written in set builder notation. We just write “”.
o A domain of , x 

 k would be: { x | x 

2
2
o A domain of , x  k would be: { x | x  k }
o A range of [–1, 1] would be: { y | y  1 }
 k }
o A range of (–, –1]  [+1, +) would be: { y | y  1 }
If k is an integer, k = … , –3, –2, –1, 0, 1, 2, 3, … , then …
Odd Multiples of

x=
k = –3
k = –2
k = –1

2

2

2
  3  

  2   

  1  


k=0
k=1
k=2
k=3
2
2

2

2

2
2
2
2
  0  
 1  

  2 

  3  

2
2
2

2
 k
Integer Multiples of 
x = k

6
5

2
2
 3  
3

4
3

2
2
 2   
2

2


2
2
 1   

2
0

2
 0  
0

2 3

2
2
1   

4 5

2
2
 2    2

6
7

2
2
 3   3
Graphs of Reciprocal Trigonometric Functions
Sine and Cosecant
Cosine and Secant
Tangent and Cotangent
The graphical images on these handouts have been produced with the TI–84 Plus Silver Edition, which is the
new calculator on the market. If you have an older model of graphing calculator, your graphs for tangent,
cosecant, secant, and cotangent MAY have vertical lines in them that make them look funny.
Below are the graphs for tangent and secant using the default mode settings in MODE. Notice that both of
these graphs contain vertical lines where the function is undefined. Your calculator is not graphing asymptotes,
but rather, connecting the dots across the view screen going across left to right.
If we change the MODE setting from Connected to Dot these extra lines will disappear and the graphs will be
more accurately represented.
```