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What is the midline equation of

{:[y=-5cos(2pi x+1)-10?],[y=]:}

What is the midline equation of\newliney=5cos(2πx+1)10?y= \begin{array}{l} y=-5 \cos (2 \pi x+1)-10 ? \\ y=\square \end{array}

Full solution

Q. What is the midline equation of\newliney=5cos(2πx+1)10?y= \begin{array}{l} y=-5 \cos (2 \pi x+1)-10 ? \\ y=\square \end{array}
  1. Identify Vertical Shift: The midline of a trigonometric function is the horizontal line that represents the average value of the maximum and minimum values of the function. To find the midline of the given function y=5cos(2πx+1)10 y = -5\cos(2\pi x + 1) - 10 , we need to identify the vertical shift of the cosine function, which is indicated by the constant term at the end of the function.
  2. Determine Midline: The constant term in the given function is 10-10. This term represents the vertical shift of the cosine function. Since the cosine function oscillates above and below this line, the midline is the horizontal line y=10 y = -10 .
  3. Final Midline Equation: We do not need to consider the amplitude or the phase shift of the cosine function to determine the midline, as the midline is solely dependent on the vertical shift. Therefore, the midline equation of the given function is y=10 y = -10 .

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