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What is the midline equation of

{:[y=cos((2pi)/(3)x)+2?],[y=]:}

What is the midline equation of\newliney=cos(2π3x)+2?y= \begin{array}{l} y=\cos \left(\frac{2 \pi}{3} x\right)+2 ? \\ y=\square \end{array}

Full solution

Q. What is the midline equation of\newliney=cos(2π3x)+2?y= \begin{array}{l} y=\cos \left(\frac{2 \pi}{3} x\right)+2 ? \\ y=\square \end{array}
  1. Midline of Trigonometric Function: The midline of a trigonometric function like y=Acos(BxC)+Dy = A \cdot \cos(Bx - C) + D or y=Asin(BxC)+Dy = A \cdot \sin(Bx - C) + D is the horizontal line y=Dy = D, where DD is the vertical shift from the x-axis.
  2. Vertical Shift in the Given Function: In the given function y=cos(2π3x)+2y = \cos\left(\frac{2\pi}{3}x\right) + 2, the value of DD is 22, which represents the vertical shift of the cosine function.
  3. Midline Equation of the Given Function: Therefore, the midline equation of the given function is y=2y = 2.

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