Trigonometric identities

problem

Polar Flower

Age

16 to 18

Challenge level

This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.
article
What Are Complex Numbers?

This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and their derivatives and proves that e^(i pi)= -1.
interactivity
Round and Round a Circle

Age

14 to 16

Challenge level

Can you explain what is happening and account for the values being displayed?
article
Why Stop at Three by One

Beautiful mathematics. Two 18 year old students gave eight different proofs of one result then generalised it from the 3 by 1 case to the n by 1 case and proved the general result.