MAC1114 Lecture Note Outlines_Eichler
Lecture 7 (L7): Graphs of Other Trigonometric Functions
Textbook Section: 4.6
Review:
1
MAC1114 Lecture Note Outlines_Eichler
Graph of Tangent:
Recall the relationship between sine, cosine, and tangent is ____________________________.
The tangent function is undefined at values for which ____________________________ is
___________________. Tangent is an ________________________ function, so the graph will be
symmetric about the ______________________.
𝜋
𝜋
Problem: Consider the tangent function on the interval [− 2 , 2 ]. What will the graph of
tangent look like?
The period of tangent is ________________________________.
The domain is ___________________________________________.
The range is _____________________________________________.
The function has vertical asymptotes at _____________________________________.
2
MAC1114 Lecture Note Outlines_Eichler
Graph of Cotangent:
Recall the relationship between sine, cosine, and cotangent is
____________________________. The cotangent function is undefined at values for which
____________________________ is ___________________. Cotangent is an ________________________ function,
so the graph will be symmetric about the ______________________.
Problem: Consider the cotangent function on the interval [0 , 𝜋]. What will the graph of
cotangent look like?
The period of cotangent is ________________________________.
The domain is ___________________________________________.
The range is _____________________________________________.
The function has vertical asymptotes at _____________________________________.
3
MAC1114 Lecture Note Outlines_Eichler
Graph of Cosecant:
Recall the relationship between sine and cosecant is ____________________________.
The cosecant function is undefined at values for which ____________________________ is
___________________. Cosecant is an ________________________ function, so the graph will be
symmetric about the ______________________.
Problem: Consider the cosecant function on the interval [−𝜋 , 𝜋]. What will the graph of
cosecant look like?
The period of cosecant is ________________________________.
The domain is ___________________________________________.
The range is _____________________________________________.
The function has vertical asymptotes at _____________________________________.
4
MAC1114 Lecture Note Outlines_Eichler
Graph of Secant:
Recall the relationship between cosine and secant is ____________________________.
The secant function is undefined at values for which ____________________________ is
___________________. Secant is an ________________________ function, so the graph will be
symmetric about the ______________________.
𝜋
𝜋
Problem: Consider the secant function on the interval [− 2 , 2 ]. What will the graph of
secant look like?
The period of secant is ________________________________.
The domain is ___________________________________________.
The range is _____________________________________________.
The function has vertical asymptotes at _____________________________________.
5
MAC1114 Lecture Note Outlines_Eichler
Problem: How do the constants 𝑎, 𝑏, 𝑐, and 𝑑 affect the graphs of
𝑓(𝑥) = 𝑑 + 𝑎 tan(𝑏𝑥 − 𝑐)
𝑓(𝑥) = 𝑑 + 𝑎 cot(𝑏𝑥 − 𝑐)
𝑓(𝑥) = 𝑑 + 𝑎 csc(𝑏𝑥 − 𝑐)
𝑓(𝑥) = 𝑑 + 𝑎 sec(𝑏𝑥 − 𝑐)
6