Circles and periodic functions

Many physical phenomena are repetitive; that is they happen in a regular cycle or with a known frequency. From things as obvious as the rising and falling of the tides to critical phenomena as increase in blood pressure with the systolic-diastolic heart rhythm, these patterns can be modelled mathematically.

To model these, we use the so called “circular” functions – sine, cosine, tangent and their inverse co-functions. These functions are better described a Periodic functions, because while they can be generated from the horizontal and vertical components of a circle, they are not circular, or even wavelike when plotted, but simple up and down movement, or oscillation.

The website, “Betterexplained” has an excellent article about the non-circular nature of periodic functions.  Read it!

If you need a review of radian measure, and the use of pi in angles, try this web page.

Here are some supplemental notes that support your development of understanding of applications of periodic functions:

01 Basic Trigonometric functions

02 Graphs of trigonometric functions

03 Graphs of trigonometric functions

04 Modelling periodic behaviour

And finally, here are some videos that explain it if you are stuck:

Here is the rest of the playlist.

And remember – start your understanding out of class, and look for clarifications (BY ASKING QUESTIONS!!!) in class.

See you in class!

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4 Comments on “Circles and periodic functions”

  1. Hao Le Says:

    Will we be going over this topic briefly or in depth?

    • CyberChalky Says:

      Hi Hao,

      This subject is later in the year for you; this post is for the Year 12 Mathematical Methods. We will be introducing the topic, but not quite as in depth.
      Feel free to read it and ask questions – it’s good practice for later studies.

  2. Patrick Says:

    Sir in the methods book, exercise 6M
    it gives us all this info about the double angle formula’s,and addition formula’s
    but in the actual exercise there are absolutely no questions relating to it at all (only that involving the use of the identity)

    So it got me wondering if it would be in the exams, cause i know that, if the examiners wanted they could put on our exam a question relating to double angle formula’s, & addition formula’s. That would be painful if no-one got any practice.


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