Question

помогите с алгеброй пример e,f,g

Answer 1

$1); ; ctga=-7; ,\\frac{3pi}{2} textless a textless 2pi ; ; Rightarrow ; ; ; sina textless 0; ,; ; cosa textgreater 0; ,; ; tga textless 0\\1+ctg^2a=frac{1}{sin^2a}; ; Rightarrow ; ; ; sin^2a= frac{1}{1+ctg^2a} =frac{1}{1+49}=frac{1}{50}=0,02\\sina=-sqrt{0,02}=-frac{sqrt2}{10}\\cosa=+sqrt{1-sin^2a}=sqrt{1-0,02}=sqrt{0,98}=frac{sqrt{98}}{10}=frac{7sqrt2}{10}\\tga=frac{sina}{cosa}=-frac{sqrt2}{10}:frac{7sqrt2}{10}=-frac{1}{7}$

$2); ; sina=-frac{2}{3}\\frac{3pi}{2} textless a textless 2pi ; ; Rightarrow ; ; ; cosa textgreater 0,; tga textless 0; ,ctga textless 0$

$cosa=+sqrt{1-sin^2a}=sqrt{1-frac{4}{9}}=sqrt{frac{5}{9}}=frac{sqrt5}{3}\\tga=frac{sina}{cosa}=-frac{2}{3}:frac{sqrt5}{3}==-frac{2}{3}cdot frac{3}{sqrt5}=- frac{2}{sqrt5}\\ctg=frac{1}{tga}=-frac{sqrt5}{2}$

$3); ; tga=-2; ,; ; 0 textless a textless frac{3pi}{2}\\Tak; kak; tga textless 0; ,; to; ; frac{pi}{2} textless a textless pi ; Rightarrow ; ; cosa textless 0,; sina textgreater 0,; ctga textless 0.\\1+tg^2a=frac{1}{cos^2a}; ; Rightarrow ; ; ; cos^2a=frac{1}{1+tg^2a}=frac{1}{1+4}=frac{1}{5}\\cosa=- frac{1}{sqrt5}\\sina=+sqrt{1-cos^2a}=sqrt{1-frac{1}{5}}=frac{2}{sqrt5}\\ctga=frac{1}{tga}=-frac{1}{2}$