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What is the midline equation of {:[y=-8cos((3pi)/(2)x+1)?],[y=◻]:}

What is the midline equation of\newliney=−8cos⁡(3π2x+1)?y=□ \begin{array}{l} y=-8 \cos \left(\frac{3 \pi}{2} x+1\right) ? \\ y=\square \end{array}

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Q. What is the midline equation of\newliney=−8cos⁡(3π2x+1)?y=□ \begin{array}{l} y=-8 \cos \left(\frac{3 \pi}{2} x+1\right) ? \\ y=\square \end{array}
  1. Finding the Midline: The midline of a trigonometric function like a cosine or sine function is the horizontal line that passes through the middle of the maximum and minimum values of the function. To find the midline, we need to look at the vertical shift of the function.
  2. General Form of a Cosine Function: The general form of a cosine function is y=Acos⁡(Bx+C)+Dy = A\cos(Bx + C) + D, where AA is the amplitude, BB is the frequency, CC is the phase shift, and DD is the vertical shift. The midline is represented by the equation y=Dy = D.
  3. No Explicit Vertical Shift: In the given function y=−8cos⁡(3π2x+1)y = -8\cos\left(\frac{3\pi}{2}x + 1\right), there is no explicit vertical shift written, which means D=0D = 0. Therefore, the midline equation is simply y=0y = 0.

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