Question

найдите sin a, tg a, ctg a, если cos a = -0.4

Answer 1

sin a = ± $sqrt{1 - cos^{2} a}$ = ± $sqrt{1 - (- 0,4)^{2} }$ = ± $sqrt{1 - 0,16}$ = ± $sqrt{0,84}$ = ± $sqrt{frac{84}{100} }$ = ± $sqrt{frac{21}{25}}$ = ± $frac{sqrt{21}}{5}$

tg a = $frac{sin a}{cos a}$ = ± $frac{sqrt{21} }{5}$ : (- 0,4) = ± $frac{sqrt{21} }{5}$ · $(- frac{10}{4})$ = ± $frac{sqrt{21} }{2}$

ctg a = $frac{1}{tg a}$ = 1 : (± $frac{sqrt{21} }{2}$) = 1 · (± $frac{2}{sqrt{21}}$) = ± $frac{2}{sqrt{21} }$