### Video Transcript

What is the midline of π¦ equals five over four cos of ππ₯ over seven minus five plus 12?

Letβs think about a few things. The midline is the horizontal centre line about which the function oscillates above and below. The midline is parallel to the π₯-axis. And the midline is affected by vertical translations.

When our curve is written in this format, π¦ equals π΄ times cos of π΅ times π₯ minus πΆ plus π·. π΄ is the amplitude, π΅ is the frequency, πΆ is the horizontal shift, and π· is the vertical shift.

Our function π¦ equals five over four times cos times π over seven π₯ minus five plus 12 has a vertical shift of positive 12. Which means it has a midline at the line π¦ equals 12. If this is the line π¦ equals 12. And this cosine function is going to oscillate above and below this midline.