Question 111
Alex picks his favorite point $(x, y)$ in the first quadrant on the unit circle $x^{2}+y^{2}=1$, such that a ray from the origin through $(x, y)$ is $\theta$ radians counterclockwise from the positive $x$-axis. He then computes $\cos^{-1}\left(\frac{4x+3y}{5}\right)$ and is surprised to get $\theta$. What is $\tan(\theta)$?