Answer
$-\dfrac{\sqrt{3}}{2}$
Work Step by Step
RECALL:
(1)The reference angle of a given angle is equal to the smallest acute angle that the terminal side makes with the x-axis.
(2) Based on the location of the terminal side of an angle $\theta$, the reference angle can be found using the formula:
(i) Quadrant I: $\theta$
(ii) Quadrant II: $180^0-\theta$
(iii) Quadrant III: $\theta-180^o$
(iv) Quadrant IV: $360^o-\theta$
The given angle is in Quadrant IV.
Use the formula in (iv) above to find its reference angle:
$=360^0-300^o
\\=60^o$
Note, however, that $300^o$ is i Quadrant IV, where sine is negative.
Thus,
$\sin{300^o} = -\sin{60^o}$
$60^o$ is a special angle whose sine value is $\dfrac{\sqrt{3}}{2}$.
Thus,
$\sin{300^o} = -\dfrac{\sqrt{3}}{2}$
