1. 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)

2. Lesson 1: The Graph of Cosine
Graph y = cos x for -2π ≤ x ≤ 2π. Use red ink.
1. |A| =
2. Period, 2π/B =
3. Interval for 5 Key Points: Period/4 =
x1: , x2: , x3: , x4: , x5:
4. 5 Key Points:
(x1, y1)= (x2, y2)= (x3, y3)= (x4, y4)= (x5, y5)=

3. y = cos x Domain Range Period Max. Min. y = -½ cos 2x Odd/Even
Observations
y = cos x
y = -½ cos 2x
Domain
Range
Period
Odd/Even
Max.
Min.

4. Lesson 2: Graphing Variations of y = A cos Bx
Use blue ink to graph y = -½ cos 2x.
1. |A| =
2. Period, 2π/B =
3. Interval for 5 Key Points: Period/4 =
x1: , x2: , x3: , x4: , x5:
4. 5 Key Points:
(x1, y1)= (x2, y2)= (x3, y3)= (x4, y4)= (x5, y5)=

5. Lesson 2: Graphing Variations of y = A cos Bx
Use blue ink to graph y = -½ cos 2x.
1. |A| =
2. Period, 2π/B =
3. Interval for 5 Key Points: Period/4 =
x1: , x2: , x3: , x4: , x5:
4. 5 Key Points:
(x1, y1)= (x2, y2)= (x3, y3)= (x4, y4)= (x5, y5)=

6. y = cos x Domain Range Period Max. Min. y = -½ cos 2x Odd/Even
Observations
y = cos x
y = -½ cos 2x
Domain
Range
Period
Odd/Even
Max.
Min.

7. 1. Find the 5 Key Points of y = -2 sin x and graph over -π ≤ x ≤ 3π.
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.

8. Answers to 4.5(a): 1. 2.

9. Answers to 4.5(b): 1. 2.