Given:
[tex]\theta[/tex] is an angle in quadrant IV that has reference [tex]\dfrac{\pi}{3}[/tex].
To find:
The value of [tex]\sin \theta[/tex].
Solution:
We know that only cos and sec are positive in quadrant IV and all other trigonometric ratios are negative in quadrant IV.
Since [tex]\theta[/tex] is an angle in quadrant IV that has reference [tex]\dfrac{\pi}{3}[/tex], therefore the value of [tex]\sin \theta[/tex] must be negative.
[tex]\sin \theta=-\sin \dfrac{\pi}{3}[/tex]
[tex]\sin \theta=-\dfrac{\sqrt{3}}{2}[/tex]
Therefore, the required value is [tex]\sin \theta=-\dfrac{\sqrt{3}}{2}[/tex].
