Step-by-step explanation:
(-5, - 12) lies on the terminal side of angle [tex] \theta [/tex]
[tex] \therefore \: ( - 5 \: - 12) = (x \: y) \\ r = \sqrt{ {x}^{2} + {y}^{2} } \\ = \sqrt{ {( - 5)}^{2} + {( - 12)}^{2} } \\ = \sqrt{25 + 144} \\ = \sqrt{169} \\ r= 13 \\ \\ \sin \theta = \frac{y}{r} = - \frac{12}{13} \\ \\ \cos \theta = \frac{x}{r} = - \frac{5}{13} \\ \\ \tan \theta = \frac{y}{x} = \frac{ - 12}{ - 5} = \frac{12}{5} \\ \\ \csc \theta = \frac{r}{y} = - \frac{13}{12} \\ \\ \sec \theta = \frac{r}{x} = - \frac{13}{5} \\ \\ \cot \theta = \frac{x}{y} = \frac{ - 5}{ - 12} = \frac{5}{12} [/tex]
