Graphs of Tangent, Cotangent, Secant, and Cosecant Functions

The trigonometric functions of tan x, cot x, sec x, and csc x can be rewritten as ratios of cos x, sin x, and 1. The functions vertical asymptotes and x-intercepts can be determined with the ratios they represent. The x-intercepts are the x values that make the numerator = 0. The vertical asymptotes are the x values that make the denominator = 0. There x-intercepts and vertical asymptotes repeat every period.      

Tangent
The function f(x) = tan x can be rewritten as f(x) = sin x/cos x. The function of tan x has vertical asymptotes at the inputs that make cos x = 0 and x-intercepts at the inputs sin x = 0. The function has symmetry along the origin making it odd.
Domain: 
Range:
Vertical asymptotes: 
Period: 
X-intrecepts: 
Y-intercept: 0

http://amsi.org.au/ESA_Senior_Years/SeniorTopic2/2d/2d_2content_6.html

Cotangent
The function f(x) = cot x can be rewritten as f(x) = cos x/sin x. The function of cot x has vertical asymptotes at the inputs that make sin x = 0 and x-intercepts at the inputs that make cos x = 0. The function has symmetry along the origin making it odd.
Domain:
Range: 
Vertical Asymptotes:
Period:
X-intercepts:
Y-intercept: none

http://www.intmath.com/trigonometric-graphs/4-graphs-tangent-cotangent-secant-cosecant.php

Secant 
The function f(x) = sec x can be rewritten as f(x) = 1/ cos x. The function of Sec x does not cross the x axis having a constant numerator of 1. It has vertical asymptotes at the inputs that make cos x = 0. Like the function of cos x the function of sec x has symmetry along the y-axis making it an even function.
Domain: 
Range:
Vertical asymptote:
Period:
X-intercepts: none
Y-intercept: o

http://jwilson.coe.uga.edu/emt668/EMAT6680.2000/Umberger/EMAT6690smu/Day6/Day6.html

Cosecant
The function f(x) = csc x = 1/ sin x Like f(x) = sec x, f(x) = csc x does not cross the x axis having a constant numerator of 1. It has a vertical asymptotes the inputs that make sin x = 0. The function has symmetry along the origin making it odd.
Domain:
Range:
Vertical asymptote:
Period: 
X-intercepts: none
Y-intercept: none

http://jwilson.coe.uga.edu/emt668/EMAT6680.2000/Umberger/EMAT6690smu/Day6/Day6.html