Answer
$- \dfrac{\sqrt 3}{2}$
Work Step by Step
Let us consider
$f( \theta)=\sin \theta$ and $\theta=60^{\circ}$
We know from the unit circle that
$\sin (60^{\circ})=\sin (\dfrac{\pi}{3})=\dfrac{\sqrt 3}{2}$
Since, $\sin$, $\csc$, and $\tan$ are odd trigonometric functions, it follows that $f (-x)=f(x) \implies \sin(-x)=- \sin(x)$
Thus, we have: $ f (-\theta)= \sin (-60^{\circ})
\\=- \sin 60^{\circ} \\=- \sin (\dfrac{\pi}{3}) \\ =- \dfrac{\sqrt 3}{2}$
