f  x   cot x
f  x   cot x
Similar to tan x
f  x   cot x
cos x
cot x 
sin x
Will occur at every point that
sin x equals zero
x  2
x  
x0
Asymptotes will
occur at every point
that the sin x
equals zero
x 
x  2
x  2
x  
x0
x  k
x 
x  2
Where k is an integer
f  x   cot x
PERIOD = 
x  k
Where k is an integer
f  x   cot x
PERIOD = 
x  k
Where k is an integer
Half-way through the cycle the function equals zero
f  x   cot x
PERIOD = 
x  k
Where k is an integer
Half-way through the cycle
the function equals zero
Half-way between the zero
and the asymptote, the value
of the function is negative
one and one
f  x   cot x
PERIOD = 
x  k
Where k is an integer
Half-way through the cycle
the function equals zero
Half-way between the zero and the asymptote,
the value of the function is one and negative one
3
y  cot x
5
3
y  cot x
5
a. Increasing or decreasing
decreasing
b. Regular, skinny or fat
Regular
c. Period

d. Phase Shift
3
5
5

3
None
e. Vertical Shift None
3
y  cot x
5
x  k
3
x  k
5
Asymptotes of cot x
5

3
3
5
x  k 
3
5
5
xk
3
5
x
3
k  1
5
xk
3
k 0
k 1
x0
5
x
3
Half-way
through the
cycle the
function
equals zero
8
6
4
2

5
3

5
6
-2
-4
-6
-8
5
6
5
3
Half-way
between the
zero and the
asymptote,
the value of
the function
is negative
one and one
3 

y  4 cot  3 x 

4 

3 



y  4 cot  3 x 
  4 cot 3  x  
4 
4


a. Increasing or decreasing
Negative sign flips it over
b. Regular, skinny or fat
c. Period
d. Phase Shift
e. Vertical Shift
increasing
3 



y  4 cot  3 x 
  4 cot 3  x  
4 
4


a. Increasing or decreasing
increasing
Negative sign flips it over
b. Regular, skinny or fat
c. Period

3
d. Phase Shift

e. Vertical Shift
4

None
Skinny
3 

y  4 cot  3 x 

4 

x  k
3
3x 
 k
4
Asymptotes of cot x
4
3
3x 
 k
4
4
12x  3  4k
12x  4k  3
1

4
12 x    4k  3
x

12
 4k  3 
1

4
7
x
12
k  1
x

12
 4k  3 
k 0
k 1
x

4
x

12
Half-way
through the
cycle the
function
equals zero
8
6
4
2
7 
Half-way
between the
zero and the
asymptote,
the value of
the function
is one and
negative one
12
 5
12

3

4

6

12
-2
-4
-6
-8

12

6

3
Half-way
through the
cycle the
function
equals zero
8
6
4
2
Negative sign flips it over
7 
Half-way
between the
zero and the
asymptote,
the value of
the function
is one and
negative one
12
 5
12

3

4

6

12
-2
-4
-6
-8

12

6

3
Half-way
through the
cycle the
function
equals zero
8
6
4
2
Negative sign flips it over
7 
Half-way
between the
zero and the
asymptote,
the value of
the function
is one and
negative one
12
 5
12

3

4

6

12
-2
-4
-6
-8

12

6

3