Step-by-step explanation:
[tex]cos \: x = \frac{3}{5} = \frac{x}{y} \\ \implies \: x = 3 \: \: and \: \: r = 5 \\ \because \: {y} = \pm\sqrt{ {r}^{2} - {x}^{2} } \\ = \pm\sqrt{ {5}^{2} - {3}^{2} } \\ = \pm\sqrt{25 - 9} \\ = \pm \sqrt{16} \\ \therefore \: y = \pm4 \\ \because \: x \: lies \: in \: {4}^{th} \: quadrant \\ \therefore \: y = - 4 \\ \\ \because \: sin \: x = \frac{y}{r} \\ \\ \huge \red{ \boxed{ \therefore \: sin \: x = \frac{ - 4}{5}}} \\ \\ \because \: tan \: x = \frac{y}{x} \\ \\ \huge \purple{ \boxed{\therefore \: tan \: x = \frac{ - 4}{3} }}[/tex]
