Chapter 4.5
Graphs of Tangent, Cotangent, Secant, and Cosecant
Learning Target: I can generate the graphs
for tangent, cotangent, secant, and cosecant.
Tangent Function
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f(x) = tan (x)
D: all real numbers except odd multiples of П/2
R: all real numbers
Continuous
Increasing on each interval in the domain
Symmetric with respect to the origin (odd)
Not Bounded
No extrema
No horizontal asymptotes
Vertical asymptotes: x = k•(П/2) for all odd integers k
End behavior DNE (hence no horizontal asymptotes)
Take a look at the graph of tangent. Why do the
vertical asymptotes occur where they do?
Take a look at the graph of cotangent. Why do the
vertical asymptotes occur where they do?
Take a look at the graph of Secant. Why do the
vertical asymptotes occur where they do?
Take a look at the graph of Cosecant. Why do the
vertical asymptotes occur where they do?
Homework
Pg. 401
# 3 – 39 every 3rd