### Trigonometry: Triangles to Functions

Package of problems

## Suggestion

Throughout, $A$, $B$ and $C$ are the angles of a triangle.

For each of the following, decide whether it is an identity (true for all triangles) or an equation (there is a triangle for which it is not true).

If it is an identity, true for all triangles, then you should prove it (perhaps using trigonometric identities that you already know).

If it is an equation, then at the very least you should give an example of a triangle for which it is not true. You could also try to solve the equation (that is, find all triangles for which it is true).

To help you decide whether an expression is an equation or an identity, you could test it out on some particular triangles, perhaps using angles where you can easily evaluate the expression, or perhaps using particular types of triangle (isosceles or right-angled or equilateral, for example).

You might find it helpful to note down any properties of trigonometric functions or trigonometric identities that you know, so that you can think about which, if any, might be helpful at any given moment.