Archive for April 2011

Circles and periodic functions

April 29, 2011

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

(more…)

Advertisements

How Mr. G stole your Holidays…

April 10, 2011

So, you’ve read the story about the Grinch stealing christmas – or you’ve seen the movie, or you’re looking up wikipedia to find out about it right now.

Well, I’m not going to let a cartoon story book character have all the fun, so here are the work that you must have completed by the start of week two. This means that you could choose to do no work through the holidays, and try and finish it all after you return to school…

Of course, I don’t recommend that strategy – it is better to spread it out through the holidays and ask for help when you need it. Post a comment on this post if you need help!

Check each of the subjects below to see what you must have finished by the above deadline!

Mathematical Methods Units 3 & 4

  1. Read the posts on Circular Functions (1, 2)
  2. Complete Book checks 1 – 3 (chapters 3, 4, 5)
  3. Complete Maths Online Skill Revision Assignment (THIS IS A WORK REQUIREMENT!)
  4. Complete all unfinished Maths Online (THIS IS A WORK REQUIREMENT!)
  5. Complete last SAC re-do task
  6. Print out the Book Check 4 (Chapter 6).

Physics Units 1 & 2

  1. Complete Electricity Practical Report
  2. Update your Lab record (it should include Circuit demo, Two CUPs (current & voltage), 3 Practicals (Ohm’s Law, Current Dividers and Voltage Dividers)
  3. The circuit simulator is here.
  4. Complete the explanatory sentences for each CUP (Current & Voltage worksheets) (1 sentence for each dial reading)
  5. Complete Hewitt Worksheets (Radiation & Circuits)
  6. Complete Questions in supplemental notes for radiation.
  7. Notes for Electricity will be inserted here shortly. Read them!
  8. Update your electricity mindmap.
  9. Upload your comment about circuits to this post

Year Enrichment Mathematics

  1. Update your Bound reference.
  2. Checklist for chapters 1 & 2
  3. Complete Mathematics Online Assignment.

Enjoy the rest of your holidays!