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