Solution:
Consider the following information:

and

by definition, this means that:

now, to find sin(θ), we must first apply the Pythagorean theorem to find the opposite side:
![\text{opposite side = }\sqrt[]{3^2-2^2}\text{ = }\sqrt[]{5}](https://img.qammunity.org/2023/formulas/mathematics/college/bfy9xbcvzaey8ipy6ump8f1x9ndboq2q2c.png)
now, since tan θ < 0 and cos θ > 0, then, the angle must be in the second quadrant, thus sin θ < 0 and it is:
![\sin (\theta)=-\frac{opposite\text{ side}}{hypotenuse}=-\frac{\sqrt[]{5}}{3}](https://img.qammunity.org/2023/formulas/mathematics/college/jqa76h6sywqlnlf2dsnhzek9rzpf43h9ad.png)
So that, we can conclude that the correct answer is:
![-\frac{\sqrt[]{5}}{3}](https://img.qammunity.org/2023/formulas/mathematics/college/kiyo81lbbb1scw3wcwq84p8t2f94slz0rv.png)