Question

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

What is the exact value of sinθ in simplified form?

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
`(\sqrt 11)/(6).`

Step-by-step explanation: Given that
`\cos \theta=(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√(1-\cos^2\theta).`

Since sine of an angle is positive in the 1st quadrant, so we have

`\sin \theta=√(1-\cos^2\theta)=\sqrt{1-(25)/(36)}=\sqrt{(11)/(36)}=(√(11))/(6).`

Thus, the answer is
`(√(11))/(6).`