### Weekly Challenge 5: Trigger

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

How would you design the tiering of seats in a stadium so that all spectators have a good view?

# Weekly Challenge 3: Geometric Trig

##### Stage: 5 Short Challenge Level:

In this diagram OA is a radius of a unit circle. The hypotenuse of the large triangle is tangent to the circle at A.

Find the lengths $\cos(a)$, $\sin(a)$, $\tan(a)$, $\frac{1}{\cos(a)}$, $\frac{1}{\sin(a)}$  and $\frac{1}{\tan(a)}$ in the diagram.

Find the areas of all of the regions in the diagram.

Did you know ... ?

Whilst trigonometric functions are defined algebraically in more advanced applications, geometric images such as this one can give great insight into the relationships between the functions. They also impart a sense of the beauty and interconnectedness of mathematics, which inspires many students of mathematics.