An operation maps the point $(x, y)$ on to the point $(x cos \theta, y sin \theta)$.
i) Find the value of $\theta$ for which the y-axis is the image of the line $y = x$.
ii) Draw a diagram to show the locus of the image of the point $(2, 2)$ as $\theta$ increases from $0^\circ$ to $90^\circ$.
Hint: What is the graph of $x = a \cos t, y = a \sin t$?