#### Answer

$\{ \ 270^{o}\ \}$

#### Work Step by Step

For a point on the unit circle, the coordinates are
($\cos\theta,\sin\theta)$, $\theta\in[0^{o},360^{o})$
To solve the problem, find the points for which
the $y$-coordinate is $-1$, ($\sin\theta=-1$)
Using the given unit circle, we find
$(0,-1),\ \quad $for $x=270^{o}$
Solution set: $\{ \ 270^{o}\ \}$