Step-by-step explanation:
Terminal arm of the angle passes through the point (-2, 11) = (x, y)
[tex]r = \sqrt{ {x}^{2} + {y}^{2} } \\ = \sqrt{ {( - 2)}^{2} + {11}^{2} } \\ = \sqrt{4 + 121} \\ = \sqrt{125} \\ = 5 \sqrt{5} \\ \\ sin \beta = \frac{y}{r} = \frac{11}{5 \sqrt{5} } \\ \\ cos\beta = \frac{x}{r} = \frac{ - 2}{5 \sqrt{5} } = - \frac{ 2}{5 \sqrt{5} } \\ \\ tan \beta = \frac{y}{x} = \frac{11}{ - 2} = - \frac{11}{2} \\ \\ cosec \beta = \frac{r}{y} = \frac{5 \sqrt{5} }{11 } \\ \\ sec\beta = \frac{r}{x} = \frac{5 \sqrt{5}}{ - 2} = - \frac{5 \sqrt{5}}{ 2} \\ \\ cot \beta = \frac{x}{y} = \frac{ - 2}{ 11} = - \frac{2}{11} [/tex]
