Trigonometric Tangram Activity

Introduction

A tangram is a Chinese puzzle square that is cut into seven pieces to be combined into various figures.

The study of trigonometry begins with triangles, and mainly right angled triangles.

There are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant and cotangent:

(note the short form for cosecant is either csc or cosec, but not cos which is used for cosine)

Trigonometric tangram

Activities

1. Figure out the construction of the sides of the above diagram.

2. Click here to download a WORD file of the above diagram and print the page out.

3. Cut the tangram into 7 pieces and move them round to make as many trigonometric identities as you can.

4. Here are some hints for making identities: You can use Pythagoras theorem. You can use ratios of sides of similar triangles. You can use the sum of lengths of sides of triangles. You should check the validity of your identities. It is more fun to play this game with your friends.

5. If you can make 10 identities : Good.

If you can make more than 15 identities : Excellent.