Download PCH Notes 4.5b

Date:
4.5(b) Notes: Graphs of Cosine
Lesson Objective: To understand the graph of y
= cos x and its variations.
CCSS: F-TF Extend the domain of trigonometric
functions using the unit circle.
You will need: 2 colored pens (red, blue)
Lesson 1: The Graph of Cosine
Graph y = cos x for -2π ≤ x ≤ 2π. Use red ink.
1.
2.
3.
x1:
|A| =
Period, 2π/B =
Interval for 5 Key Points: Period/4 =
, x2:
, x3:
, x4:
4.
5 Key Points:
(x1, y1)=
(x2, y2)=
(x3, y3)=
(x4, y4)=
, x5:
(x5, y5)=
Observations
Domain
Range
Period
Odd/Even
Max.
Min.
y = cos x y = -½ cos 2x
Lesson 2: Graphing Variations of y = A cos Bx
Use blue ink to graph y = -½ cos 2x.
1.
2.
3.
x1:
|A| =
Period, 2π/B =
Interval for 5 Key Points: Period/4 =
, x2:
, x3:
, x4:
4.
5 Key Points:
(x1, y1)=
(x2, y2)=
(x3, y3)=
(x4, y4)=
, x5:
(x5, y5)=
Lesson 2: Graphing Variations of y = A cos Bx
Use blue ink to graph y = -½ cos 2x.
1.
2.
3.
x1:
|A| =
Period, 2π/B =
Interval for 5 Key Points: Period/4 =
, x2:
, x3:
, x4:
4.
5 Key Points:
(x1, y1)=
(x2, y2)=
(x3, y3)=
(x4, y4)=
, x5:
(x5, y5)=
Observations
Domain
Range
Period
Odd/Even
Max.
Min.
y = cos x y = -½ cos 2x
4.5(a): Do I Get It? Yes or No
1. Find the 5 Key Points of y = -2 sin x and
graph over -π ≤ x ≤ 3π.
2. Find the 5 Key Points of y = 3 sin 2x and
graph over 0 ≤ x ≤ 2π.
4.5(b): Do I Get It? Yes or No
1. Find the 5 Key Points of y = -3 cos π/2 x and
graph over -4 ≤ x ≤ 4.
2. Find the 5 Key Points of y = 2 cos ½x and
graph over 0 ≤ x ≤ 2π.
Answers to 4.5(a):
1.
2.
Answers to 4.5(b):
1.
2.