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Weekly Challenge 43: A Close Match

Can you massage the parameters of these curves to make them match as closely as possible?

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Weekly Challenge 44: Prime Counter

A weekly challenge concerning prime numbers.

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Weekly Challenge 28: the Right Volume

Can you rotate a curve to make a volume of 1?

Weekly Challenge 21: Trig Identity

Stage: 4 and 5 Short Challenge Level: Challenge Level:1

 
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.