1)Найти [latex]sin alpha [/latex] и [latex]tg alpha [/latex], если [latex]cos alpha =- frac{2}{5} [/latex] и [latex] pi extless alpha extless frac{3 pi }{2} [/latex] 2) Найти [latex]cos alpha [/latex] и [latex]ctg alpha [/latex], если [latex]sin alpha = frac{3}{4} [/latex] и [latex] frac{ pi }{2} extless alpha extless pi [/latex]

[latex]1); ; cos alpha =-frac{2}{5}; ,\\sin alpha =pm sqrt{1-cos^2 alpha }; ,; tg alpha =pm sqrt{frac{1}{cos^2 alpha }-1}\\; ; alpha in (pi ;frac{3pi}{2}); ; o ; ; sin alpha extless 0,; ; tg alpha extgreater 0\\sin alpha =-sqrt{1-frac{4}{25}}=-sqrt{frac{21}{25}}=-frac{sqrt{21}}{5}\\tg alpha =+sqrt{frac{25}{4}-1}=frac{sqrt{21}}{2}[/latex][latex]2); ; sin alpha =frac{3}{4}\\ alpha in (frac{pi}{2};pi ); ; o ; ; cos alpha extless 0; ,; ; ctg alpha extless 0\\cos alpha =-sqrt{1-sin^2 alpha }=-sqrt{1-frac{9}{16}}=-frac{sqrt7}{4}\\ctg alpha =-sqrt{frac{1}{sin^2 alpha }-1}=-sqrt{frac{16}{9}-1}=-frac{sqrt7}{3} [/latex]