Graph of the Tangent Function
The tangent function is odd, therefore the graph y=tanx is symmetric with respect to the origin.
tan(θ) =sin(θ)/cos(θ)
tangent is then undefined when cosx=0. When there is a zero in the denominator, you put a vertical asymptote there.
The vertical asymptotes will be at
–π/2, π/2, and3π/2
Tangent will be zero when the numerator Sinx=0. The x intercepts will then be at 0, π, 2π, - π, -2π
The period for tangent functions is
![](webkit-fake-url://48FBFCDD-9C30-4DA2-83D9-8719BE1926B5/image.tiff)
therefore for
y=tanx, the period is
π
Graph of the Cotangent Function
Lets start with
y=cotx=
Cosx/Sinx
Because Sinx=0 would make the function undefined, values that make it Sinx=0 will be the Vertical Asymptotes.
The vertical asymptotes are at -2π, -π, π, 2π
Because Cosx=0 would make Cotangent 0, values that make Cosx=0 will be the X-Intercepts
The x-intercepts will be –π/2, π/2, and3π/2
y=cotx, the period is
π
Graphs of Secant functions
secx=
1/cosx
The asymptotes of
secx will be the same of
tanx, which are -
,
,
3π/2, -3π/2
It is important to draw out the reciprocal function and take the reciprocals of the y-coordinate to obtain points for the graph.
The period would be still 2
![](http://www.regentsprep.org/Regents/math/algtrig/ATT7/otherg90.gif)
Because secx is even, it will be centered around the origin.
Graphs of Cosecant functions
cscx=
1/sinx
The asymptotes of
cscx will be the smae of
cotx which are
–π/2, π/2, and3π/2
It is important to draw out the reciprocal function and take the reciprocals of the y-coordinate to obtain points for the graph.
Period is still
2
π
Because cscx is odd, the graph will be centered around the origin.