MathNet 2001 — Part 01 Question 147

The graph of $x^{2}-(y-1)^{2}=1$ has one tangent line with positive slope that passes through $(x, y)=(0,0)$. If the point of tangency is $(a, b)$, find $\sin ^{-1}\left(\frac{a}{b}\right)$ in radians.