Building blocks

## Problem

Take a look at triangle $OPQ$ in this diagram. Explain why $P$ has the coordinates given.

Imagine we move $P$ by increasing $\angle QOP$, whilst keeping $PQ$ perpendicular to the $x$-axis.

How could $P$ move if

1. the length of $OP$ is fixed but $Q$ can move along the $x$-axis as required?

2. $Q$ remains fixed but the length of $OP$ can change?

In each case, can you express the coordinates of $P$ in terms of $\angle QOP$ ?