4.6(a) Notes: Graph of the Tangent Function Date: 4.6(a) Notes: Graph of the Tangent Function   Lesson Objective: To understand the graph of y = tan x and its variations. CCSS: F-TF Extend the domain of tri­go­no­me­tric functions using the unit circle. You will need: Colored pens

Lesson 1: The Graph of Tangent Graph y = tan x for -π/2 ≤ x ≤ π/2 on a coor­­dinate plane. Use red ink for this first graph.     

x Lesson 1: The Graph of Tangent – y = tan x Deg. ° y=tan x 3 4 6 π -π      x -π 2   -5π 12 3 4 6 π 5π Deg. ° y=tan x  

Lesson 1: The Graph of Tangent     

Lesson 1: The Graph of Tangent Observations: 1. Domain: 2. Range:   Observations: 1. Domain: 2. Range: 3. Period: 4. Odd or Even Function?: 5. Vertical Asymptotes: 6. x-int: 7. y = 8.   

Lesson 2: The Graph of Tangent – The Shortcut!   Graphing y = A tan (Bx – C): A. Asymptotes: Bx – C = -π/2 and Bx – C = π/2 B. x-intercept: Midpoint between asymptotes x = -Asymp.+ Asymp. 2 C. y = -A: Midpt between left asymp and x-int x = -Asymp.+ x-int. ; y = -A D. y = A: Midpt btwn x-int and right asymp x = x-int.+ Asymp. ; y = A   

Lesson 2: Graphing y = A tan Bx   Graph y = 3 tan 2x in blue ink for -π/4 ≤ x ≤ 3π/4 on the same coor­dinate plane from Lesson 1.   

= Asymp: Bx – C = -π/2 Bx – C = π/2 x-intercept: x = + = 2 y = -A: Lesson 2: Graphing y = 3 tan 2x Asymp: Bx – C = -π/2 Bx – C = π/2 x-intercept: x = + = 2 y = -A: x = + = y = A: x = +    =    

Lesson 2: The Graph of Tangent – The Shortcut!   Graph y = 3 tan 2x in blue ink for -π/4 ≤ x ≤ 3π/4 on the same coor­dinate plane from Lesson 1.   

Lesson 3: Graphing y = tan (Bx – C)   Graph two full periods of y = tan (x – π/2) in purple or black ink on the same coor­dinate plane from Lessons 1 and 2.   

= Asymp: Bx – C = -π/2 Bx – C = π/2 x-intercept: x = + = 2 y = -A: Lesson 2: Graphing y = tan (x – π/2) Asymp: Bx – C = -π/2 Bx – C = π/2 x-intercept: x = + = 2 y = -A: x = + = y = A: x = +    =    

Lesson 3: Graphing y = tan (Bx – C)   Graph two full periods of y = tan (x – π/2) in purple or black ink on the same coor­dinate plane from Lessons 1 and 2.   

4.6(a): Do I Get It? Yes or No 1. Graph y = 2 tan x/2 over -π < x < 3π. 2. Graph two full periods of y = tan (x + π/4).