Section 5-4
1
Math 150 Lecture Notes
More Trigonometric Graphs
The tangent and cotangent functions have period π:
tan (x + π) = tan x cot (x + π) = cot x
The cosecant and secant functions have period 2π:
csc (x + 2π) = csc x sec (x + 2π) = sec x
The functions y = a tan kx and y = a cot kx (k > 0) have period
k
π
.
The functions
y
=
a
csc
kx
and
y
=
a
sec
kx
(
k
> 0) have period
k
π
2.
Example 1: Find the period and graph the function f(x) = -3 sec x
Example 2: Find the period and sketch the graph of g(x) = 3 csc
+
2
π
x.
