Trig identity

In this short challenge, can you use angle properties in a circle to figure out some trig identities?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

 

 
Image
Trig identity

In this diagram $O$ is the centre of a unit circle (i.e. a circle with radius 1).

Use it to find two trigonometrical relationships 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.