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Grade 11 - history of trigonometry project - Louise Keegan

Module by: Wynberg Girls' High School. E-mail the author

Summary: A project on the history of trigonometry

GRADE 11: MATHEMATICS: History of trigonometry project

Instructions:

  • Ensure that you meet the requirements for both sections of the project.
  • You may present your work creatively, but please ensure that your project will be able to fit in your portfolio.
  • Please attach the marking rubric to the back of your project.
  • You may work with a friend, but you each have to hand in your own work. (Please indicate if you have worked with a partner on the rubric.

The aim of this project is to investigate the development of trigonometry throughout the ages. I hope that this gives you a broader knowledge of this branch of mathematics and helps you to see some of the context that it fits into.

Section A

You must draw a timeline that shows the development of trigonometry through the ages. You will find that there is a lot of information about the history of trigonometry available. Below are some concepts, formulae and Mathematicians that should be on your timeline.

You need to show when the following concepts first became recognized:

  • Measuring angles
  • Trilateromeny
  • 360 degrees in a circle
  • Observing ratios/lengths using chords in circles
  • First trigonometric tables
  • Plimpton 322
  • sine and cosine (versine)
  • tangent
  • Optional: you can show different cultures’ contributions to trig tables
  • Using the words sine and cosine
  • Treating trigonometry as a separate discipline of Mathematics
  • Defining trigonometric ratios in terms of triangles and not circles
  • Modern abbreviations for sin, cos and tan

You need to show when the following formulae were found (all of these form part of your school Mathematics syllabus, note that π2=90°π2=90°%pi over 2 = 90^{circ}):

* hypotenuse2=side2+side2hypotenuse2=side2+side2hypotenuse^2 = side^2 + side^2 or c2=a2+b2c2=a2+b2c^2 = a^2 + b^2

* sin2(x)+cos2(x)=1sin2(x)+cos2(x)=1sin^2(x) + cos^2(x) = 1

* sin(x)=cos(90°−x)sin(x)=cos(90°−x)sin(x) = cos(90^{circ} - x)

* 1−sin2(x)=cos2(x)=sin(90°−x)1−sin2(x)=cos2(x)=sin(90°−x)1 - sin^2(x) = cos^2(x) = sin(90^{circ} - x)

* tan(x)=sin(x)cos(x)tan(x)=sin(x)cos(x)tan(x) = {sin(x)} over {cos(x)}

* sin(2x)=2sin(x)cos(x)sin(2x)=2sin(x)cos(x)sin(2x) = 2 sin(x) cos(x)

* sinAa=sinBb=sinCcsinAa=sinBb=sinCc{sin A} over a = {sin B} over b = {sin C} over c

Some names that should be mentioned are listed below. Include why these people are important – you may find that they discovered a concept or formulae listed above. It has been shown that there were different cultural contributions to trig, you may want to indicate which group of people these mathematicians belonged to (e.g. Babylonian, Egyptian, Greek/Hellenistic, Indian, Islamic, Chinese, European)

  • Abu al-Wafa al-Buzjani
  • Ahmes
  • Aryabhata
  • Brahmagupta
  • Euler
  • Georg Joachim Rheticus
  • Hipparchus of Nicea
  • Muhammad ibn Jabir al-Battini (Albatenius)
  • Muhammad ibn Musa al-Khwaritmi
  • Ptolemy
  • Regiomontanus
  • Varahamihira

Section B

Answer all of the following questions. You may use your timeline to help you.

  • What do you think was the very first recorded step in the development of trig functions?
  • Who do you think should be given the title “The founder of trigonometry”? Why?
  • On your timeline, what do you think is the most important fact? Why?
  • What did you find to be the most interesting or surprising thing that you learned from this exercise?
  • Where does the word sine come from?
  • Where did you get your information (list all the resources you used)? Which resource/ site was the most helpful in completing this project? Why?

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