Answer:
[tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]
Step-by-step explanation:
If θ is in Quadrant III
[tex]\cos\theta=-\dfrac{2}{3}[/tex]
As we know in III quadrant cosine and sine both are negative.
using trigonometry identity
[tex]\sin\theta=-\sqrt{1-\cos^2\theta}[/tex]
[tex]\sin\theta=-\sqrt{1-(\frac{2}{3})^2}[/tex]
[tex]\sin\theta=-\sqrt{1-\frac{4}{9}}[/tex]
[tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]
Hence, The value of [tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]
