Answer: The answer is \(\dfrac{\sqrt 11}{6}.\)
Step-by-step explanation: Given that \(\cos \theta=\dfrac{5}{6}\) and \(\theta\) lies in the first quadrant. We are to find the exact value of \(\sin \theta\) in simplified form.
We know that
\(\sin^2\theta+\cos^2\theta=1\\\\\Rightarrow \sin \theta=\pm\sqrt{1-\cos^2\theta}.\)
Since sine of an angle is positive in the 1st quadrant, so we have
\(\sin \theta=\sqrt{1-\cos^2\theta}=\sqrt{1-\dfrac{25}{36}}=\sqrt{\dfrac{11}{36}}=\dfrac{\sqrt{11}}{6}.\)
Thus, the answer is \(\dfrac{\sqrt{11}}{6}.\)
