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[Trigonometric Graphs]

Use the following information to write an equation of the graph described:

7. sin; Amp = 2, per = π, vertical shift = down 3.

8. cos; Amp = 1; per = π/4, phase shift = left π.

Explain.​

Respuesta :

tramserran

Answer: 7. y = 2 sin (2x) - 3

              [tex]\bold{8.\quad y=sin\bigg(8x + \dfrac{8}{\pi}\bigg)}[/tex]

Step-by-step explanation:

The general form of a sine equation is: y = A sin (Bx - C) + D    where

  • Amplitude = |A|
  • Period (P) = [tex]\dfrac{2\pi}{B}[/tex]
  • Phase Shift = [tex]\dfrac{C}{B}[/tex]
  • Vertical Shift = D (positive is up, negative is down)

7. Given:

  • A = 2
  • P = π = [tex]\dfrac{2\pi}{B}[/tex]  → B = 2
  • C = 0 (none)
  • D = -3

--> y = 2 sin (2x) - 3

8. Given:

  • A = 1
  • P = [tex]\dfrac{\pi}{4}[/tex] = [tex]\dfrac{2\pi}{B}[/tex]  → B = 8
  • [tex]\text{Phase Shift = }-\pi = \dfrac{C}{8}\implies C = -8\pi[/tex]
  • D = 0 (none)

[tex]\implies y=sin\bigg(8x + \dfrac{8}{\pi}\bigg)[/tex]

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