Question

If θ is in Quadrant III and cosθ -2/3, then sinθ = _____.

Answer 1

In 3rd quadrant, sine function is negative.
So, sin theta = sqrt(1-(2/3)^2) = - sqrt(5) / 3

Answer 2

`\sin\theta=-(√(5))/(3)`

Explanation:

If θ is in Quadrant III

`\cos\theta=-(2)/(3)`

As we know in III quadrant cosine and sine both are negative.

using trigonometry identity

`\sin\theta=-√(1-\cos^2\theta)`

`\sin\theta=-\sqrt{1-((2)/(3))^2}`

`\sin\theta=-\sqrt{1-(4)/(9)}`

`\sin\theta=-(√(5))/(3)`

Hence, The value of
`\sin\theta=-(√(5))/(3)`