Transcript 6.7

6.7
Graphing other Trigonometric
Functions
Graphs of the Tangent,
Cotangent, Secant, and
Cosecant Functions
The Graph of y = tan x
x
y
1.73
(0, 0)
1
0
1.73
1

What happens as x approaches 2 ?

What happens as x approaches  2 ?
5
x
2
x
3
x
2

2
3
5
3
x
2
0
3
x
5

2
5
x
2
Characteristics of the Tangent Function
1. The domain is the set of all real numbers, except
odd multiples of  2.
2. The range consists of all real numbers.
3. The tangent function is an odd function (symmetric
with respect to the origin).
4.
5.
Characteristics of the Tangent Function
6.
x0

3
 ,2
6
5

0
 ,1
6 2

3

5
3

 ,2
3


 ,1
3 2
5
0
3

5
x0
3
5

0
 2 ,0
3

 , 3
6
5
Find the values.
• a. tan(9π/2)
• b. cot(7π/2)
Graph
  
y  csc    2
 2 4
a. Graph the equation
b. What happens at t = 15?
 
y  6 tan t 
 30 
Here we go again…
• Write an equation for a secant function
with period π, phase shift π/3, and vertical
shift -3.