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Introducing Trigonometry

August 30, 2012

I have a year 11 class taking the Higher, Modular GCSE this coming year. It’s been a while since I’ve taught higher so I’m quite looking forward to it.

Rather than just give them the trig functions and let them practise, I’m going to see if they can discover at least some of it for themselves.

So, here’s an introductory prezi

<div class=”prezi-player”><style type=”text/css” media=”screen”>.prezi-player { width: 550px; } .prezi-player-links { text-align: center; }</style><div class=”prezi-player-links”><p>Investigating Circles on Prezi</p></div></div>

Depending on how it goes, I’ll hopefully draw out:
  • That the value for Sine 60 is the same regardless of the circle (or triangle) size,
  • That the value for Sine x changes depending on x
  • Sine x is between 0 and 1 [for x between 0 and 90]
  • I’d like to graph what we find
  • Some may ask about Sine of x greater than 90 or less than 0
  • Some may start to consider Cosine or Tangent

While not amazingly exciting, I’m hoping this will be a little more interesting than giving them the rules to follow.

As is so often the case when trying to find a good way to teach something, I’ve found out something new. Why is it called Sine? Well since you asked:

Etymologically, the word sine derives from the Sanskrit word for chord, jiva*(jya being its more popular synonym). This was transliterated in Arabic as jiba ??????????????, abbreviated jb ???????????? . Since Arabic is written without short vowels, “jb” was interpreted as the word jaib ??????????????, which means “bosom”, when the Arabic text was translated in the 12th century into Latin by Gerard of Cremona. The translator used the Latin equivalent for “bosom”, sinus (which means “bosom” or “bay” or “fold”) [7][8] The English form sine was introduced in the 1590s.
Taken from wikipedia.

I shall enjoy telling them that when they inevitably ask!

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  1. Garrod permalink

    Thank you Dave. I like the idea of using Prezi the visuals work very well. Also I have no doubt my yr 11’s will also love the derivation of the term sin…..Also for an extension Task, using the angle defined from ox half line rotated around the origin, enables you to use Pythagoras’ Thm within the generated triangle (o*2+a*2=h*2) to create the identity sin*2 + cos*2 = 1Cheers,Garrod

  2. Anonymous permalink

    <html><head></head><body bgcolor="#FFFFFF"><div>Thanks Garrod.&nbsp;</div><div>I’m going to try and include a little more prezi this year.&nbsp;</div><div><br></div><div>I’ll prob try the extension you suggest in a couple of weeks time.&nbsp;<br><br></div></body></html>

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