FREQUENCY AND PHASE SHIFTS Section 7 4 PreCalculus

FREQUENCY AND PHASE SHIFTS Section 7. 4 Pre–Calculus AB Pre–AP/Dual, Revised © 2014 viet. dang@humble. k 12. tx. us 1/7/2022 1: 59 AM 7. 3: Amplitude and Vertical Shifts 1

TRANSFORMATION OF GRAPH EQUATION A. Equation: y = A trig function B(x – c) + d B. A is the vertical stretch/compression or Amplitude for Sine and Cosine C. B is the period D. C is the horizontal shift or phase shift E. D is the vertical shift F. Frequency is defined as the number of cycles per second 1/7/2022 1: 59 AM 7. 3: Amplitude and Vertical Shifts 2

STEPS 1/7/2022 1: 59 AM 7. 3: Amplitude and Vertical Shifts 3

REVIEW OF GRAPHS 1/7/2022 1: 59 AM 7. 3: Amplitude and Vertical Shifts 4

TRIG TABLES FOR MAIN TRIG FUNCTIONS y = csc (x) C Und 1 1/7/2022 1: 59 AM y = sec (x) Und C y = cot (x) C Und 1 1 Und 0 – 1 – 1 Und Und 7. 3: Amplitude and Vertical Shifts 5

EXAMPLE 1 y =y y– 2 tan ==– 2 tan tan(x) (x) – 1 –π –π Und – 3π/4 – 1 21 –π/2 C 0– 1 –π/4 – 2 – 3 1 00 Und 1/7/2022 1: 59 AM Amplitude Period Phase Shift Spacing (A. P. ) Vertical Shift 7. 3: Amplitude and Vertical Shifts 6

EXAMPLE 2 y = csc (x) –π/2 Und π/2 C 1 3π/2 Und 5π/2 – 1 7π/2 Und 1/7/2022 1: 59 AM Amplitude Period Phase Shift Spacing (A. P. ) Vertical Shift 7. 3: Amplitude and Vertical Shifts 7

YOUR TURN y = sec (x) – 5π/4 Und –π 1 Amplitude Period Phase Shift – 3π/4 Und –π/2 – 1 –π/4 Und 1/7/2022 1: 59 AM Spacing Vertical Shift 7. 3: Amplitude and Vertical Shifts 8

ASSIGNMENT Worksheet 1/7/2022 1: 59 AM 7. 3: Amplitude and Vertical Shifts 9