Answer:
- 0.183
Step-by-step explanation:
Given that [tex]\sin \theta = \frac{1}{3}[/tex]
and [tex]\frac{\pi }{2} < \theta < \pi[/tex]
We have to find the exact value of [tex]\sin (\theta + \frac{\pi }{6} )[/tex].
Now, [tex]\sin \theta = \frac{1}{3}[/tex]
⇒ [tex]\theta = \sin ^{-1} (\frac{1}{3} ) = 19.47[/tex]
Now, since [tex]\frac{\pi }{2} < \theta < \pi[/tex],
So, [tex]\theta = 180 - 19.47 = 160.53[/tex]
{Since [tex]\sin \theta = \sin (180 - \theta)[/tex]
Now, [tex]\theta + \frac{\pi }{6} = 160.53 + 30 = 190.52[/tex]
Hence, [tex]\sin (\theta + \frac{\pi }{6} )[/tex].
= [tex]\sin 190.52[/tex]
= - 0.183 (Approximate) (Answer)
