Question

Daca x∈(0, π/2) si cos x=3/5, calculati sin x!

Answer 1

(sin x)^2 + (cos x)^2=1=>(sin x)^2 =1-(cos x)^2 =1-$(\frac{3}{5}) ^{2} = \frac{16}{25}$. => sin x = $\frac{4}{5}$ si sin x = -$\frac{4}{5}$ 

Dar x∈(0, π/2) => sin x >=0 => singura solutie e sin x = $\frac{4}{5}$ 

Answer 2

$sin^{2}x + cos^{2} x = 1 =\ \textgreater \ sin^{2}x = 1 - cos^{2}x =\ \textgreater \ sin^{2}x = 1 - \frac{3}{5} =$ $= \ \textgreater \ sin^{2} x = 1 - (\frac{3}{5} )^{2}$ $= \ \textgreater \ sin^{2} x = 1 - \frac{9}{25} = \ \textgreater \ sin^{2} x = \frac{25-9}{25} =\ \textgreater$ sin^{2} x =  \frac{16}{25} = >   [tex]sinx = +/- \sqrt{ \frac{16}{25} } =\ \textgreater \ sinx = -/+ \frac{4}{5} =\ \textgreater \ sinx = 4/5 x∈(0, π/2)[/tex]