If tan θ = $$-\frac{12}{5}$$​, then the value of sin θ is:

Correct option is C

Given:

​$$\tan \theta = \frac{-12}{5}$$​​

Concept Used:​​

​$$\tan \theta = \frac{\sin \theta}{\cos \theta}$$​​

Given:

​$$\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{-12}{5}$$​​

let's consider the opposite side to be -12 and the adjacent side to be 5 (negative sign indicates the angle is in the second or fourth quadrant).

Using the Pythagorean theorem:

​$$\text{Hypotenuse} = \sqrt{(-12)^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13$$​​

​$$\sin \theta = \frac{-12}{13}, \quad \cos \theta = \frac{5}{13}$$​​

​$$\sin \theta = \frac{-12}{13}$$​​