WRITING TRIG FUNCTIONS Section 7 4 PreCalculus AB
WRITING TRIG FUNCTIONS Section 7. 4 Pre-Calculus AB Pre-AP/Dual, Revised © 2014 viet. dang@humble. k 12. tx. us 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 1
TRANSFORMATION GRAPH EQUATION A. B. C. D. E. F. Equation: y = A trig function B(x – h) + k A is the amplitude B is the period h is the horizontal shift or phase shift k is the vertical shift Frequency is defined as the number of cycles per second 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 2
STEPS FOR TRANSFORMATION GRAPH EQUATION A. Identify the amplitude (a) (|above point| + |below point|/2) B. Identify the period (b) 1. Counting the number of hills from 0 to 2π OR 2. Find the length of the curve to get the period C. Identify the horizontal shift (h) for sine and cosine and move over the parent function D. Identify the vertical shift (k) by drawing a horizontal line cutting the graph in half 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 3
AMPLITUDE Amplitude (a) the maximum or minimum vertical distance between the graph and the x-axis. Amplitude is always positive. 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 4
PERIOD 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 5
EXAMPLE 1 Write the equation of the graph below using a sine function 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 6
EXAMPLE 1 A Write another equation of the graph below using a cosine function. 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 7
EXAMPLE 1 A Write another equation of the graph below using a cosine function. 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 8
EXAMPLE 1 A Write another equation of the graph below using a cosine function. 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 9
EXAMPLE 2 Write the equation of the graph below using a sine and cosine function 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 10
YOUR TURN Write the equation of the graph below using a sine function 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 11
EXAMPLE 3 Write the equation of the graph below using a cosine function 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 12
EXAMPLE 4 Write the equation of the graph below using a sine and cosine function 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 13
YOUR TURN Write the equation of the graph below using a cosine function 2/2/2022 2: 53 AM 7. 4 A: Frequency and Phase Shifts 14
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