transforming trig functions

Transcription

1 transforming trig functions Ch.6 Lesson 4 7 1

2 Target Agenda Purpose Evaluation TSWBAT write equations for trig functions given amplitude, period and phase shift, write equations given a graph, and graph an equation. Warm-Up/Homework Check #1,2, packet discuss answers to trig packet Transformation lesson BAT use prior knowledge to understand something new, set up a formula from given info

3 Warm-Up: 1. You can look on your unit circle or sheet, What is the exact value of cos(270 o ) sin(7π/4) cot( 270 o ) 2. What does each variable(a,k,c,h) do to the graph: y = a(k x c) + h 3

4 What are the critical values? Relative Max: Relative Min: Asymptotes: 1-1 N/A Cosine W t Holes: N/A Domain: All real numbers Range: -1< y < 1 Using the table above, and the table in your calculator, draw the graph of cosθ, for 360 < θ < 360 4

5 What are the critical values? Relative Max: Relative Min: Asymptotes: 1-1 N/A Sine Holes: N/A Domain: All real numbers Range: -1< y < 1 Using the table above, and the table in your calculator, draw the graph of cosθ, for 360 < θ < 360 5

6 What are the critical values? Relative Max: Relative Min: Asymptotes: Holes: - every 90 o +180 o k N/A Tangent Domain: Range: All real numbers except k o o All real numbers Using the table above, and the table in your calculator, draw the graph of cosθ, for 360 < θ < 360 6

7 Larry says that the cosecant graph is like the sine graph except with the humps turned upside down. What does he mean? Does what he said make sense? Use pictures in your explanaon What did you like about this acvity? 7

8 What are the critical values? Relative Max: Relative Min: Asymptotes: Holes: Domain: Range - every 90 o +180 o k N/A Using the table above, and the table in your calculator, draw the graph of cosθ, for 360 < θ < 360 Secant All real numbers except 90 o +180 o k - < y < -1 and 1 < y < 8

9 What are the critical values? Relative Max: Relative Min: Asymptotes: Holes: Domain: Range: - every 180 o k N/A All real numbers except 180 o k - < y < -1 and 1< y < Using the table above, and the table in your calculator, draw the graph of cosθ, for 360 < θ < 360 Cosecant 9

10 What are the critical values? Relative Max: Relative Min: - Cotangent Asymptotes: Holes: every 180 o k N/A Domain: Range: All real numbers except 180 o k All real numbers Using the table above, and the table in your calculator, draw the graph of cosθ, for 360 < θ <

11 Before y = a(kx+c) 2 + b Now y = A sin(kθ c) + b 11

12 Amplitude: It is the A in y = Asinθ, is how high the humps are from the x axis (technically only for sine and cosine) If A > 0, then A is posive, and so the funcon gets stretched vercally If A < 0, then A is negave, and so the funcon is a reflecon of the parent funcon, y = A sin θ, over the x axis and stretched vertically 12

13 Example of Amplitude changing the values y = 3 cos x y = cos x amplitude: A= x y x y y = 4 cos x y =.5 cos x 13

14 Trig Transformations.notebook Period: Def: Is the value of the angles that repeat y = sin (k θ) the proof: Y = sin(kθ + 360) ) Therefore the period for sine is 360/k. What is the period for cosine? 360/k What is the period for tangent? 180/k 14

15 Example of K changing the Period Ex: y = sin(4θ), the period is 360/4 = 90 So every 90 the funcon repeats Ex. y = sin( 1 5 θ), the period is? So every the function repeats ex. if the period of a tangent function is 270 o, write the function 15

16 Evaluation: 1. What is the amplitude, period, and phaseshift of: y = 2sin(4x 4π) Pracce: pg. 373 #49 52 write equaon from a graph pg. 383 #22,23,24,228,30,31,33 from info pg. 401 #30,32,33,36 38 graph the funcon 16