Question

Given cosθ=5/6 and θ lies in Quadrant I .

Answer 1

With this, we know cos=x/r

x = 5
and
r = 6

We need to find y.

25 + y² = 36

y² = 11

y = √11

sin of theta would be √11/6

Answer 2

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 $\dfrac{\sqrt{11}}{6}.$