In the diagram at right, the point $P$ has Cartesian coordinates $\left(x, y\right)$ and polar coordinates $\left(r, θ\right)$.

1. Explain why $x = r \cos θ$.

   Hint (a):

   Using the diagram, $\cos\left(θ\right) = x/r$.

2. Find $y$ in terms of $r$ and $θ$.

   Hint (b):

   Using the diagram, $\sin\left(θ\right) =$ ?

3. Find $r$ in terms of $x$ and $y$.

   Hint (c):

   What theorem can be used to relate the three sides of a right triangle?

4. Find θ in terms of $x$ and $y$.

   Hint (d):

   Use tangent.