Graphs of Trigonometric
Functions
Graphing Other
Trigonometric Functions
Properties of
Trigonometric Graphs
•
1.
2.
3.
4.
5.
6.
7.
8.
When graphing a trigonometric function
you need to be able to identify the
properties of the graph.
Period
Amplitude
Domain
Range
X intercepts (if any)
Y intercept (if any)
Maximum and minimum points (if any)
Asymptotes (if any)
Tangent Function
y
• Remember tan θ =
. Tangent is
x
undefined at 90 degrees, 270 degrees,
negative 90 degrees, etc. It is undefined for
any multiple of 90 degrees.
• Therefore it has asymptotes at these
points. Thus it’s domain is the set of real
numbers except for these points.
• Also tangent and cotangent have a period
of π whereas the other four trigonometric
functions have a period of 2π
Properties
From the video, we can now state the properties
of the graph y = tan x
1. Period is π
2.
Domain: Set of all real numbers except
π
2
n
where n is an odd integer.
3. Range: Set of all real numbers
4. X intercepts are located at
5. The y intercept is 0
6. The asymptotes are
odd integer.
πn
x=
where n is an integer.
π
2
n
where n is an
Reciprocal Relationship
• The sine and cosecant functions are
reciprocal functions.
• The cosine and secant functions are
reciprocal functions
• The tangent and cotangent functions
are reciprocal functions.
Cosecant
• Let’s look at another video and
determine the graph of
cosecant, the reciprocal of sine.
Period Formula
• The period of functions
y = sin kθ , y = cos kθ ,
y = sec kθ , y = csc kθ
2π
is
, where k > 0
k
• The period of functions
y = tan kθ
and y = cot kθ
is
π
k
where k > 0
HW # 48
• Section 6-7
• Pp. 400-403
• # 8, 9, 29, 30,
31,
• 33, 37, 39, 52,
54
Work with your partner
* Find each value by referring to
the graphs of the trigonometric
functions.
1. Tan 7π/2
2. cot 3π/2
3. Write an equation for a secant function with a period
of 3π , phase shift π/2 , and vertical shift 3.
Find the values of x for which each equation is true.
4. csc x = 1
5. sec x = 1
6. Graph y = csc (2θ – π/2) + 1
(Hint: make the
vertical shift first)