Question

Daca a€(0.π/2) si sin(a)=3/5.Calculati tg a/2.

Answer 1

$sin^{2} x+cos^{2} x=1 \\ cos^{2}x =1- sin^{2} x \\ cos x= \sqrt{1- sin^{2}x } ~(a~se~afla~in~cadranul~1~deci~sina\ \textgreater \ 0~;cosa\ \textgreater \ 0) \\ cosx= \sqrt{1- \frac{9}{25} } \\ cosx= \ \sqrt{ \frac{25-9}{25} } \\ cosx= \sqrt{ \frac{16}{25} } \\ cosx= \frac{4}{5} \\ tg \frac{a}{2}= \frac{sina}{1+cosa} \\ tg \frac{a}{2}= \frac{ \frac{3}{5} }{1+ \frac{4}{5} } \\ tg \frac{a}{2}= \frac{3}{5}* \frac{5}{5+4} \\ tg \frac{a}{2} = \frac{3}{5}*,\frac{5}{9} \\ tg \frac{a}{2}=\frac{1}{3} \\ Sper~ca~te-am~ajutat!$