
Trigonometry 

Graphs of
Trigonometric Functions 
The
Graph of the Cotangent Function f
(x) = cotx 
Properties of the
cotangent function 
Domain and range 
Zeros of the cotangent
function 
Parity and periodicity
of the cotangent function 
The
cotangent function behavior
and monotony 






Graphs of
trigonometric functions 
The
graph of the cotangent function f
(x) = cot
x 
By associating the values of the cotangent of arcs of the unit circle, to corresponding arcs in a coordinate
system obtained are points
P (x,
cot x)
of the graph of the cotangent function.

The graph of the cotangent function in
the down figure is drawn using the relation between tangent and cotangent
which states,

cot
x = 
tan (x + p/2). 


Properties of the
cotangent function 
 Domain 
From the definition,
cot x = cos
x/sin
x, follows that all real numbers
x, as input values, associate exactly
one functional value as output, except the zeroes of the sine function from the denominator, thus 
D_{f} = R \ {kp,
k Î
Z}.

 Range
f (D) = R
or 
oo < cot x < + oo. 
 Zeros of the
cotangent
function 
The zeroes of the cotangent are determined by the zeroes of the cosine function
from the numerator, thus 
x = p/2
+ kp,
k Î
Z.


Parity
and periodicity 
The cotangent is
an odd function since 

The cotangent is periodic function with the period
p = p
since for every arc x
from the domain 
cot
(x + kp) =
cot x. 

Behavior of the cotangent function
(monotonicity) 
The cotangent is decreasing function in every interval between any of the two successive vertical
asymptotes 
that
is, f (x_{1})
> f (x_{2})
for all x_{1} <
x_{2}.

The vertical asymptotes are,
x = kp,
k Î
Z.










Trigonometry
contents A 



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