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'Weekly Challenge 21: Trig Identity' printed from http://nrich.maths.org/

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In this diagram $O$ is the centre of a unit circle. Use it to find a trigonometrical relationship between $A$ and $2A$.
 
 
 
Did you know ... ?

Trigonometrical expressions can often be derived algebraically or geometrically. In more advanced applications the functions of trigonometry are defined as infinite power series rather than geometric ratios.