Question

If alt="sin\theta = \frac{1}{3}" align="absmiddle" class="latex-formula"> , $\frac{\pi }{2} \ \textless \ \theta \ \textless \ \pi$. Find the exact value of
$sin (\theta + \frac{\pi }{6})$

Answer 1

Answer:

- 0.183

Step-by-step explanation:

Given that $\sin \theta = \frac{1}{3}$

and $\frac{\pi }{2} < \theta < \pi$

We have to find the exact value of $\sin (\theta + \frac{\pi }{6} )$.

Now, $\sin \theta = \frac{1}{3}$

⇒ $\theta = \sin ^{-1} (\frac{1}{3} ) = 19.47$

Now, since  $\frac{\pi }{2} < \theta < \pi$,

So, $\theta = 180 - 19.47 = 160.53$

{Since $\sin \theta = \sin (180 - \theta)$

Now, $\theta + \frac{\pi }{6} = 160.53 + 30 = 190.52$

Hence, $\sin (\theta + \frac{\pi }{6} )$.

= $\sin 190.52$

= - 0.183 (Approximate) (Answer)