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Frequency and Phase Shifts

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Presentation on theme: "Frequency and Phase Shifts"— Presentation transcript:

1 Frequency and Phase Shifts
Section 7.4 Pre–Calculus AB Pre–AP/Dual, Revised ©2014 4/7/ :30 PM 7.3: Amplitude and Vertical Shifts

2 Transformation of Graph Equation
Equation: y = A trig function B(x – c) + d A is the vertical stretch/compression or Amplitude for Sine and Cosine B is the period C is the horizontal shift or phase shift D is the vertical shift Frequency is defined as the number of cycles per second 4/7/ :30 PM 7.3: Amplitude and Vertical Shifts

3 7.3: Amplitude and Vertical Shifts
Steps Identify A to D Identify the Period by using the equation, π 𝑩 for Tangent and Cotangent and 𝟐π 𝑩 for the others Identify the Anchor Points (spacing) by 𝑷𝒆𝒓𝒊𝒐𝒅 𝟒 Identify “C”, the trig function, and the table for each trig function Put “C” as the vertical shift and follow the table For Sine and Tangent, use the horizontal shift when the first y = 0 For Cosine and Secant, use the horizontal shift when the first y = 1 For Cosecant and Cotangent, use the horizontal shift when the first y = undefined 4/7/ :30 PM 7.3: Amplitude and Vertical Shifts

4 7.3: Amplitude and Vertical Shifts
Review of Graphs 4/7/ :30 PM 7.3: Amplitude and Vertical Shifts

5 Trig Tables for Main Trig Functions
y = csc (x) C Und 1 –1 y = sec (x) Und C 1 –1 y = cot (x) C Und 1 –1 4/7/ :30 PM 7.3: Amplitude and Vertical Shifts

6 7.3: Amplitude and Vertical Shifts
Example 1 Graph 𝒚=−𝟐𝐭𝐚𝐧 𝒙+ 𝝅 𝟐 −𝟏 in one period and identify amplitude, period, vertical shift, and phase shift y = –2tan (x) –1 –π Und –3π/4 1 –π/2 –1 –π/4 –3 y = –2tan (x) –π Und –3π/4 2 –π/2 –π/4 –2 y = tan (x) Und –1 C 1 Amplitude Period Phase Shift Spacing (A.P.) Vertical Shift 4/7/ :30 PM 7.3: Amplitude and Vertical Shifts

7 7.3: Amplitude and Vertical Shifts
Example 2 Graph 𝒚= 𝐜𝐬𝐜 𝟏 𝟐 𝒙+ 𝝅 𝟐 in one period and identify amplitude, period, vertical shift, and phase shift y = csc (x) Und C 1 –1 Amplitude Period Phase Shift Spacing (A.P.) Vertical Shift –π/2 π/2 3π/2 5π/2 7π/2 4/7/ :30 PM 7.3: Amplitude and Vertical Shifts

8 7.3: Amplitude and Vertical Shifts
Your Turn Graph 𝒚= 𝐬𝐞𝐜 𝟐 𝒙+𝝅 in one period and identify amplitude, period, vertical shift, and phase shift y = sec (x) –5π/4 Und –π 1 –3π/4 –π/2 –1 –π/4 Amplitude Period Phase Shift Spacing Vertical Shift 4/7/ :30 PM 7.3: Amplitude and Vertical Shifts

9 7.3: Amplitude and Vertical Shifts
Assignment Worksheet 4/7/ :30 PM 7.3: Amplitude and Vertical Shifts


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