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| Trigonometry |
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Graphs of
Trigonometric Functions |
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The
Graph of the Cotangent Function f
(x) = cotx |
Properties of the
cotangent function |
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Domain and range |
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Zeros of the cotangent
function |
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Parity and periodicity
of the cotangent function |
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The
cotangent function behavior
and monotony |
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Graphs of
trigonometric functions |
| The
graph of the cotangent function f
(x) = cot
x |
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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.
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| The graph of the cotangent function in
the down figure is drawn using the relation between tangent and cotangent
which states,
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| cot
x = -
tan (x + p/2). |
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| 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 |
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Df = R \ {kp,
k Î
Z}.
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| - 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 |
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x = p/2
+ kp,
k Î
Z.
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| -
Parity
and periodicity |
| The cotangent is
an odd function since |
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| The cotangent is periodic function with the period
p = p
since for every arc x
from the domain |
| cot
(x + kp) =
cot x. |
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| 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 (x1)
> f (x2)
for all x1 <
x2.
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| The vertical asymptotes are,
x = kp,
k Î
Z.
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| Trigonometry
contents A |
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| Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |
