4.3 Graphing Other Trig Functions

Graph of y = csc xReciprocal of sineGraph sine first

csc x is und when sin x = 0

csc x = 1 when sin x = 1csc x = 2 when sin x = ½ csc x = –1 when sin x = –1csc x = –2 when sin x = –½

1

–1

Amp is undefinedPeriod = 2π

You find sec x the same way!! Graph cos x first! Then take the reciprocal!

5 6

6 6 6

b

c

a

d

Per =

IL:

= 2

=

=

= 0

1

4 4

12

3

7

12

5

6

1sec 2

3 3y x

6

6

Check Period:

2 3

12 12 12

3 4

12 12

3 7

12 12

3 10

12 12

Check a point:1

,3 3

Factor out b1

sec23 6

y x

1

3

2

2

2

12

3

12

1

3

1

3

Ex 1) Graph

Graph of y = tan x

Period = π

Amplitude = 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

Diff from sin & cos!!

Diff from sin & cos!!

b

c

ad

Per =

IL:

=

=

= 2= 0

3

4

2

–2

1Period

4

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 b1

3

13

3

(middle)

Ex 2) Graph

b

c

a

d

Per = IL:

= 2

=

=

= 0

1

2 4 8

08

4

3

8

1cot 2

3 4y x

8

8

Check Period:3

8 8 2

08 8

8 8

2

8 8 8

3

8 8

Check a point:1

,4 3

(middle)

Factor out b1

cot 23 8

y x

1

3

1

3

1

3

b

2

Graph tan first

cot x is reciprocal of tan x

Ex 3) Graph

Homework

#403 Pg 205 #5, 9, 17 – 19, 21 – 24 (no graph), 26 – 28, 30, 34 – 40, 43, 44

To find asymptotes without graphing set the argument equal to where the parent graph has asymptotes and solve