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Answer :

DᴀʀᴋPᴀʀᴀᴅᴏxgo

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

The required equation is :

[tex]\qquad \sf  \dashrightarrow \:y =a \cos(bx) + k[/tex]

Now, let's find the required values :

period (p) = 6

[distance between any successive Crest or trough]

a = - 4 (flipped)

b = 2π/p = 2π/6 = π/3

k = -2

Distance of starting position from origin = k

Now, plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: - 4 \cos( \frac{\pi}{3} x) - 2[/tex]

There is not crest given so use distance between troughs

Period (T):-

  • Distance between two troughs
  • |3-(-3)|
  • 6

Frequency:-

[tex]\\ \rm\dashrightarrow \dfrac{1}{T}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{1}{6}[/tex]

[tex]\\ \rm\dashrightarrow 0.17Hz[/tex]

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