If [tex]sin\theta = \frac{1}{3}[/tex] , [tex]\frac{\pi }{2} \ \textless \ \theta \ \textless \ \pi[/tex]. Find the exact value of [tex]sin (\theta + \frac{\pi }{6})[/tex]

Answer:- 0.183Step-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)