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. |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)=
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.
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)=
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)=
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.
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.
Answers to 4.5(a): 1. 2.
Answers to 4.5(b): 1. 2.