The tangent
function, is one of the
three main trigonometry functions. The tangent of the angle
theta
is the
ratio of the
opposite side
over the
adjacent side. This ratio is the same on
any size
circle. Using the
unit
circle the ratio is equal to the
y variable
divided by the
x variable
in the
Cartesian plane. The tangent function is the
reciprocal function of the
cotangent
function. The tangent of 0 degrees and 180 degrees is equal to
zero and the tangent of 90 degree or 270 degrees approaches
infinity
on the
coordinate system. This is because the ratio
gets larger and larger as it approaches the numbers one divided by
zero.
As the
theta angle starts from 0 degrees to 90
degrees the value of its tangent increases from zero to be greater than one
at 45 degrees. The tangent is one at 45 degrees because the
x
coordinate is equal to the
y coordinate. As the
theta angle goes up to 90 degrees the tangent
goes from one to infinity. This is all in the first quadrant of the
coordinate
system. As the angle hits 90 degrees the value of the tangent gets really
large and approaches positive infinity. The angle then extends into the second
quadrant and the value of the tangent jumps from positive infinity to
negative
infinity. As the
theta angle goes from 90
degrees to 135 degrees the tangent goes from negative infinity back to negative
one. Here the value is a
negative number because the
x variable is negative. As the
theta
angle goes past 135 degrees and to 180 degrees it reaches zero again and then
enters the third quadrant. Here the tangent value increase from zero to one
again at 225 degrees. After this it increases to positive infinity as it reaches
270 degrees. Finally, in the fourth quadrant, the tangent value jumps again
to negative infinity then increases to reach zero again at 360 degrees. Any
angle beyond 360 degrees repeats the cycle. The
domain
and
range of the tangent function are both the
set
of real number.