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 · (± $\frac{2}{\sqrt{21}}$) = ± $\frac{2}{\sqrt{21} }$