Question

Fie a∈R cu tg a=2/5. Să se calculeze |sin a|.

Answer 1

$tga= \frac{sina}{cosa}= \frac{2}{5} \rightarrow cosa= \frac{5sina}{2} \\ sin^2a+cos^2a=1 \\ sin^2a+( \frac{5sina}{2})^2=1 \\ \frac{4sin^2a}{4}+ \frac{25sin^2a}{4}=1 \\ \frac{29sin^2a}{4}=1 \\ 29sin^2a=4 \\ sin^2a= \frac{4}{29} \\ |sina|= \sqrt{ \frac{4}{29} }= \frac{2}{ \sqrt{29} } = \frac{2 \sqrt{29} }{29}$