Answer
$ x=tan\theta $
$ y=tan^2\theta $
Work Step by Step
Let the coordinates of point P be given as $ P(x,y)$ and satisfy the equation $ y=x^2$ with $ x\geq0$.
Join point P with the origin (0,0) to form an angle $\theta $ with respect to the x-axis such that:
$ x=rcos\theta, y=rsin\theta $ where $ r^2=x^2+y^2$.
Plug in x and y into the parabola equation:
$ rsin\theta=r^2cos^2\theta $ so $ r=\frac{sin\theta}{cos^2\theta}$
Hence:
$ x=tan\theta $ and $ y=tan^2\theta $
