Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Cosines Rule

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

Sine and Cosine for Connected Angles

Age 14 to 16Challenge Level
The relationship between trig values for angles that are in the ratio $1:2$ is important for further study in trigonometry.

The pegboard gives a simple context in which to discover and explore this relationship.