Aim: How do we sketch y = tan x

Aim: How do we sketch y = tan x

Aim: What are the graphs of tangent function and reciprocal functions? Do Now: If y = tan x, fill in the table and then sketch the graph. x 0 /6 y 0 0.58 /4 /3 4/9 17/36 /2 1 1.73 5.67 u.d. HW: Handout

11.43 M at h Composer 1. 1. 5 http: / / www. mathcomposer. com 5 4 y y = tan x 3 2 1 -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 -1 -2 -3 -4 -5 x 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 The sine and cosine curves are continuous while the graph of y = tan x is not or discontinuous at 3

etc and the graph repeats every x ,x ,x 2 2 2 , Summary of the properties of f(x) = tan x Domain : {x x real numbers, and x ( 2 k 1) , k is integer} Range: { y real numbers} Period: 2 within which lies 1 complete curve Range: there is no range existed. Vertical asymptotes: at odd multiples of /2 M at h Composer 1. 1. 5 ht t p: // www. mat hcomposer. com 5

y y = 2 tan x 4 3 2 1 -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 -1 Period is x 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 -2 -3 -4 -5 M at h Composer 1. 1. 5 ht tp: / / www. mat hcomposer . com 5 y 4

y = 2 tan 2x 3 2 1 -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 -1 -2 -3 -4 -5 x 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Period is /2 M ath Composer 1. 1. 5 htt p: / / www. mat hcomposer. com 5 y y = tan 0.5x 4 3

2 1 -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 -1 x 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Period is 2 -2 -3 -4 -5 M at h Composer 1. 1. 5 ht tp: / / www. mat hcomposer . com 5 y 4 y = tan 0.25x 3 2 1

-2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 -1 -2 -3 -4 -5 x 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Period is 4 The general formula to find the period of tangent function is B a) Graph: y = 2sin x and y = tan x on the same axes, over x b) How many values are the solutions of tan x = 2sin x? M ath Composer 1. 1. 5 htt p: / / www. mathcomposer. com 5 y = tan x

y 4 3 2 1 . -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 -1 -2 -3 -4 -5 5 points y = 2sin x x 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 M at h Composer 1. 1. 5 ht t p: // www. mat hcomposer. com 5 y

y = cot x 4 3 2 1 -2.0 -1.5 -1.0 -0.5 x 0.5 1.0 1.5 2.0 -1 -2 -3 -4 -5 For integral values of n, the vertical lines on the graph at x = n are asymptotes Mat h Composer 1. 1. 5 ht t p: // www. mat hcomposer. com 5

y 4 3 2 1 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 y = sec x x 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 -1 -2 -3 -4 -5 For integral values of n, every /2 + n , sec x is undefined. The vertical lines on the graph at x = /2 + n are asymptotes. M at h Composer 1. 1. 5 ht tp: // www. mat hcom poser. com 5

y 4 3 2 1 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 y = csc x x 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 -1 -2 -3 -4 -5 For integral values of n, every n , csc x is undefined The vertical lines on the graph at x = n are asymptotes. What are the maximum and minimum values of the function a) y = 3 sin 2x ? b) y = 3 cos 2x ? c) y = 3 tan 2x ? a) Max. = 3, Min. = -3

b) Max. = 3, Min. = -3 c) Max. is infinity, Min. is negative infinity If f(x) = 2tan 2x, what is the value of 1. f ( ) ? 4 2. f ( ) ? 3 )? 3. f ( 2

Recently Viewed Presentations

  • Social Work and Economic Empowerment: Financial Capability in ...

    Social Work and Economic Empowerment: Financial Capability in ...

    Infuse financial capability concepts into social work education and field placements. Conduct research to identify evidence-based programs and social work interventions targeted to vulnerable populations. Expand programming by initiative beyond the SSW and UM campus
  • Material & Fabrikasi Serat Optik - Afief Dias Pambudi

    Material & Fabrikasi Serat Optik - Afief Dias Pambudi

    Terbuat dari unsur chalcogen (S, Se, Te) dan elemen lainnya seperti P, I, Cl, Br, Cd, Ba, Si, atau Tl. Diantara banyak variasi chalcogen glass . As. 2. S. 3. adalah salah satu material yang sering digunakan. Single mode fiber...
  • Latest, Greatest Assistive Technology and Other Supports for ...

    Latest, Greatest Assistive Technology and Other Supports for ...

    Latest, Greatest Assistive Technology and Other Supports for Children's Literacy Development in Inclusive Settings Patsy L. Pierce, Ph.D. Center for Literacy & Disability Studies, UNC-CH
  • Designing Experiments Experimental Methodology for Software ...

    Designing Experiments Experimental Methodology for Software ...

    An Example One Factor Experiment The Single Factor Model One Factor Experiments With Replications Sample Data for Our Example Computing Effects Calculating Calculating for Our Example Calculating j Calculating a Column Mean Calculating the Parameters Parameters for Our Example Estimating...
  • The Importance of the Legal System for the Health Professional

    The Importance of the Legal System for the Health Professional

    References/Recommendations "Cell-Level Healing" by Joyce Hawkes, PhD (Biophysics/Electron Microscopy) "Power VS Force" by David Hawkins, MD "The Biology of Belief" by Bruce Lipton, PhD (Developmental Biologist/Medical School Professor) "A Year to Live" by Stephen Levine (Founder of New York City's...
  • Christmas Tree Hill Neighborhood Response Group

    Christmas Tree Hill Neighborhood Response Group

    STEP 7: LEARN HOW TO USE YOUR 2-WAY RADIO CORRECTLY. There is a monthly radio test for all BCs. Learning the basic operating guidelines for the use of two way radios is something which is extremely important prior to use....
  • devoted very loyal; faithful mercy kindly treatment; pity ...

    devoted very loyal; faithful mercy kindly treatment; pity ...

    Juan Verdades. Review. flourish. flour - ish (verb) ... Kid friendly definition - to do or give something in return for something received. ... pity hope a feeling that one's desires will happen Last modified by: Lenovo User ...
  • MEL-Con Writing Strategy

    MEL-Con Writing Strategy

    Conclusion. The last sentence of the paragraph . Summarizes the thesis in original words. Mentions the three pieces of evidence again very briefly. AVOID: "All in all" or "In conclusion" or "Finally" or "To sum it all up"(these are overused,...