graphing tan and cot

1. Homework QuestionsHomework Questions

2. Section 4.5 Part 2Section 4.5 Part 2
Graphing tan and cotGraphing tan and cot

3. Properties of Tan(x)Properties of Tan(x)
– Period:Period:
– Domain: all real numbers except when n isDomain: all real numbers except when n is
oddodd
– Range: (-Range: (-∞, ∞)∞, ∞)
– x-int:x-int:
– y-int: 0y-int: 0
– Asymptotes: when n is oddAsymptotes: when n is odd
π
2
nπ
nπ
2
n
x
π
=

4. Graph of Tan(x)Graph of Tan(x)

5. ExamplesExamples
 Find the value or tanFind the value or tan 2
9π

6. GraphGraph 1)
3
tan(6 −+= πθ
π
y

7. GraphGraph 1)
42
tan( +−=
πθ
y

8. Properties of Cot(x)Properties of Cot(x)
– Period:Period:
– Domain: all real numbers exceptDomain: all real numbers except
– Range: (-Range: (-∞, ∞)∞, ∞)
– x-int: when n is oddx-int: when n is odd
– y-int: noney-int: none
– Asymptotes:Asymptotes:
π
2
nπ
nx π=
nπ

9. ExampleExample
 Find cot( )Find cot( )
2
7π

10. GraphGraph 3)
42
cot( −+=
πθ
y

11. HomeworkHomework
 4.5 Worksheet (tan and cot)4.5 Worksheet (tan and cot)