Answer
Coordinates: $\left(\frac{\sqrt 2}{2}, \frac{\sqrt 2}{2}\right)$
Angle: $45^{\circ}$
Work Step by Step
You are given the equations $y=x$ and $y=\sqrt {1-x^{2}}$.
Input these into a graphing calculator, and look specifically for the point of intersection between both lines.
In this case, the point of intersection is $(0.707,0.707)$ which is the same as $\left(\frac{\sqrt 2}{2}, \frac{\sqrt 2}{2}\right)$.
Then take the arcsin and arc cosine of $\frac{\sqrt 2}{2}$:
$\cos^{-1}\left(\frac{\sqrt 2}{2}\right) = 45^{\circ}$
$\sin^{-1}\left(\frac{\sqrt 2}{2}\right) = 45^{\circ}$
So, these coordinates are the cosine and sine of $45^{\circ}$.
