Precalculus
Unit 4 part II– Trigonometry Graphing
Name:
Date:
Friday February 13, 2015
Notes: Graphing Tangent & Cotangent Functions
Tangent Graphs
Since y = tan (θ ) =
sin (θ )
cos (θ )
, there are times when it is undefined.
when
x
=0
−
π
2
−
π
0
4
π
π
4
2
y = tan ( x )
y = tan ( x ) is an odd function
What are the asymptotes that are closest to the origin?
(symmetric to the
)
What is the period for the tangent curve? Find the length of one cycle (i.e. the distance between two asymptotes).
Note: This is different than for the generic sine and cosine graphs.
Tangent/Cotangent functions:
π
b
= period or b =
π
Sine/Cosine functions:
period
2π
2π
= period or b =
period
b
#1 – 3: Identify at least two asymptotes (close to the origin), period, and any reflections.
1.
⎛1 ⎞
y = tan ⎜ x ⎟
⎝2 ⎠
2.
y = 3 tan ( 2 x )
3.
Asymptotes
Asymptotes
Asymptotes
Period
Period
Period
Reflection over
x-axis
y-axis
none
Reflection over
x-axis
y-axis
none
y = −3 tan ( 2 x )
Reflection over
x-axis
y-axis
none
Cotangent Graphs
Since y = cot (θ ) =
cos (θ )
sin (θ )
, there are times when it is undefined.
when
= 0.
−
x
π
2
−
π
4
0
π
π
4
2
y = cot ( x )
What are the asymptotes that are closest to the origin?
What is the period for the cotangent curve? Find the length of one cycle (i.e. the distance between two asymptotes).
Note: This is different than for the generic sine and cosine graphs.
Tangent/Cotangent functions:
π
b
= period or b =
π
Sine/Cosine functions:
period
2π
2π
= period or b =
period
b
#4 - 5: Identify at least two asymptotes (close to the origin), period, and reflection.
4.
⎛1 ⎞
y = 2cot ⎜ x ⎟
⎝3 ⎠
5.
1
y = cot ( 2 x )
2
6.
Asymptotes
Asymptotes
Asymptotes
Period
Period
Period
Reflection over
x-axis
y-axis
none
Reflection over
x-axis
y-axis
none
π⎞
⎛
y = 2 tan ⎜ x + ⎟ − 1
2⎠
⎝
Reflection over
x-axis
y-axis
none