Question Video: Finding the Midline of a Trigonometric Function | Nagwa Question Video: Finding the Midline of a Trigonometric Function | Nagwa

Question Video: Finding the Midline of a Trigonometric Function

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

01:24

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.

Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

  • Interactive Sessions
  • Chat & Messaging
  • Realistic Exam Questions

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy