Inquiry Question Can I Create a Timeline to Show How Trigonometry Developed?

Inquiry Question Can I create a timeline to show how Trigonometry developed?

Name: ______Date: ______

General Instructions Your task is to draw a timeline that shows the development of trigonometry through the ages.

Project submission: • Submit your timeline and the answers to the questions below.

2021-08-04 Page 1 of 3

Math: Trigonometry

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 • 360 degrees in a circle • Observing ratios/lengths using chords in circles • First trigonometric tables • Plimpton 322 • sine and cosine (versine) • tangent • 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.

• hypotenuse2=side2+side2 or c2=a2+b2 • sin2(x)+cos2(x)=1 • sin(x)=cos(90∘−x) • 1−sin2(x)=cos2(x)=sin(90∘−x) • tan(x)=sin(x)/cos(x) • sin(2x)=2sin(x)cos(x) sin 퐴 sin 퐵 sin 퐶 • = = 푎 푏 푐

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, 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 2021-08-04 Page 2 of 3

Math: Trigonometry

• 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?

Sites to get you started http://en.wikipedia.org/wiki/History_of_trigonometric_functions http://aleph0.clarku.edu/~djoyce/ma105/trighist.html http://neo.math.unifi.it/archimede/archimede_NEW_inglese/trigonometria/trigonometria/prima.h tml http://en.wikipedia.org/wiki/Timeline_of_mathematics

2021-08-04 Page 3 of 3