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Answer :

DᴀʀᴋPᴀʀᴀᴅᴏxgo

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

The required equation is :

[tex]\qquad \sf  \dashrightarrow \: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]

Not passing through origin (it's cosine)

Period:-

  • Difference between any two crests
  • |-3-3|
  • |-6|
  • 6

Now

Frequency:-

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

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

[tex]\\ \rm\dashrightarrow \nu=0.167Hz[/tex]

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