Question Video: Finding the Midline of a Trigonometric Function

Video Transcript

What is the midline of 𝑦 equals five over four cos of 𝜋𝑥 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 𝑥-axis. And the midline is affected by vertical translations.

When our curve is written in this format, 𝑦 equals 𝐴 times cos of 𝐵 times 𝑥 minus 𝐶 plus 𝐷. 𝐴 is the amplitude, 𝐵 is the frequency, 𝐶 is the horizontal shift, and 𝐷 is the vertical shift.

Our function 𝑦 equals five over four times cos times 𝜋 over seven 𝑥 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.