Video: Finding the Midline of a Trigonometric Function

What is the midline of 𝑦 = (5/4) cos ((πœ‹π‘₯/7) βˆ’ 5) + 12?

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Video Transcript

What is the midline of 𝑦 equals five over four cos of πœ‹π‘₯ over seven minus five plus 12?

Let’s 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, 𝑦 equals 𝐴 times cos of 𝐡 times π‘₯ minus 𝐢 plus 𝐷. 𝐴 is the amplitude, 𝐡 is the frequency, 𝐢 is the horizontal shift, and 𝐷 is the vertical shift.

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

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