Writing Trig Functions

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Writing Trig Functions Section 7.4 Pre-Calculus AB Pre-AP/Dual, Revised ©2014 viet.dang@humble.k12.tx.us 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts

Transformation Graph Equation 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 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts

Steps for Transformation Graph Equation Identify the amplitude (a) (|above point| + |below point|/2) Identify the period (b) Counting the number of hills from 0 to 2π OR Find the length of the curve to get the period Identify the horizontal shift (h) for sine and cosine and move over the parent function Identify the vertical shift (k) by drawing a horizontal line cutting the graph in half 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts

7.4A: Frequency and Phase Shifts Amplitude Amplitude (a) the maximum or minimum vertical distance between the graph and the x-axis. Amplitude is always positive. 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts

7.4A: Frequency and Phase Shifts Period The period of a function is the x-interval needed for the function to complete one cycle. For b > 0, the period of y = a sin bx or y = a cos bx is 𝟐𝝅 𝒃 . If 0 < b < 1, the graph of the function is stretched horizontally. 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts

7.4A: Frequency and Phase Shifts Example 1 Write the equation of the graph below using a sine function 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts

7.4A: Frequency and Phase Shifts Example 1A Write another equation of the graph below using a cosine function. 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts

7.4A: Frequency and Phase Shifts Example 1A Write another equation of the graph below using a cosine function. 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts

7.4A: Frequency and Phase Shifts Example 1A Write another equation of the graph below using a cosine function. 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts

7.4A: Frequency and Phase Shifts Example 2 Write the equation of the graph below using a sine and cosine function 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts

7.4A: Frequency and Phase Shifts Your Turn Write the equation of the graph below using a sine function 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts

7.4A: Frequency and Phase Shifts Example 3 Write the equation of the graph below using a cosine function 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts

7.4A: Frequency and Phase Shifts Example 4 Write the equation of the graph below using a sine and cosine function 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts

7.4A: Frequency and Phase Shifts Your Turn Write the equation of the graph below using a cosine function 4/13/2019 4:50 PM 7.4A: Frequency and Phase Shifts