7.9 Graph of Tangent Function

Graph of y = tanx

Period = 𝝅Amplitude = not defined

und2

3 1.73

14

3.6

6 30 0

3.6

6 3

14

3 1.73

und2

x y

1

–1

2 2x

General Tangent Curve

tan ( )y a b x c d

Periodb

Horizontal Shiftc

Vertical Shiftd

middle point of graph

Ex 1) Graph

bcad

Per = IL:

= == 2= 0

3

4

2

–2

1Period

4 g

5

4

2

4

12 tan

3 2y x

12 tan

3 6y x

2

2

Check Period:2 3

2 3 5

4 4 4

3 8

4 4

2 3

4 4 4

3 4

4 4

Check a point:

,24

Factor out b

1

3

13

3

(middle)

Ex 2) Graph

bcad

Per = π IL:

= 1 == –3= 0

4

3

–3

1Period

4 g

4

2

3

4

3tan2

y x

2

0

Check Period:0

2

4 4 4

0

4

2 3

4 4 4

4

4 4

Check a point:

3, 3

4

(middle)

Graph of y = cscx

Reciprocal of sineGraph sine first

csc x is und when

sin x = 0

csc x = 1 when sin x = 1

csc x = 2 when sin x = ½

csc x = –1 when sin x = –1

csc x = –2 when sin x = –½

1

–1

Amp is undefinedPeriod = 2π

Graph of y = secx

Reciprocal of cosineGraph cosine first

sec x is und when

cos x is 0

sec x = 1 when cos x = 1

sec x = 2 when cos x = ½

sec x = –1 when cos x = –1

sec x = –2 when cos x = –½

1

–1

Amp is undefinedPeriod = 2π

Homework

#722 Pg. 454 42, 44 Pg. 465 5, 6, 15, 17, 18, 19, 22, 29 – 34 all