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Write an equation for the given function given the amplitude, period, phase shift, and vertical shift. attachment below is below, please help with this asap!

Write an equation for the given function given the amplitude, period, phase shift, and vertical shift. attachment below is below, please help with this asap! class=

Answer :

Ashraf82

The equation of the function is y = 4 sin( [tex]\frac{1}{2}[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2

Step-by-step explanation:

If the equation is y = A sin (B x + C) + D , where

  • A is the amplitude  
  • The period is 2π/B  
  • C is the horizontal shift to the left  (C is positive) or to right (C is negative)
  • D is the vertical shift  (D is positive) or down (D is negative)

∵ The amplitude is 4

A = 4

∵ The period is 4π

∴  T= 4π ⇒ T = [tex]\frac{2\pi }{B}[/tex]

∵ The phase shift is [tex]-\frac{4}{3}\pi[/tex]

C =  [tex]-\frac{4}{3}\pi[/tex]

∵ The vertical shift is -2

D = -2

Substitute these values in the y = A sin( [tex]\frac{2\pi }{T}[/tex] t + C) + D

∴ y = 4 sin( [tex]\frac{2\pi }{4\pi }[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2

- Simplify it

∴ y = 4 sin( [tex]\frac{1}{2}[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2

The equation of the function is y = 4 sin( [tex]\frac{1}{2}[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2

Learn more:

You can learn more about the trigonometric equations in brainly.com/question/2285189

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