If cos⁡x = $$\frac{-3}{5}$$ and x lies in the third quadrant, then the value of the sin x is:

Correct option is D

Given:

$$\cos x = -\frac{3}{5},$$​ , x  lies in the third quadrant.

Formula Used:

​$$\sin^2 x + \cos^2 x = 1$$​​

Solution:

​$$\sin^2 x = 1 - \cos^2 x$$​​

​$$\sin^2 x = 1 - \left( -\frac{3}{5} \right)^2\\\ \sin^2 x = 1 - \frac{9}{25}\\\ \sin^2 x = \frac{25}{25} - \frac{9}{25} = \frac{16}{25}\\\ \\\sin x = -\frac{4}{5}\quad \quad \text{(x lies in third quadrant)}$$​​

Therefore, the value of sin x is  -4/5.