Question

tgx=3/4
Aflati sin x

Answer 1

$\bold{Metoda~1} \\ \\ tg(x)= \frac{sin(x)}{cos(x)} = \frac{sin(x)}{ \sqrt{1-sin^2(x)} }= \frac{3}{4} \Rightarrow \frac{sin^2(x)}{1-sin^2(x)} = \frac{9}{16} \Rightarrow \\ \Rightarrow16 sin^2(x)=9-9 sin^2(x) \Rightarrow 25 sin^2(x)=9 \Rightarrow \boxed{ sin(x)=\frac{3}{5}}.$

$\bold{Metoda~2} \\ \\ Fie~triunghiul~ \Delta ABC ~dreptunghic~in~A~si~m(\ \textless \ B)=x \textdegree. \\ \\ AB=c~;~AC=b~;~BC=a. \\ \\ tg(x)=\frac{3}{4} \Leftrightarrow \frac{b}{c}= \frac{3}{4} \Rightarrow b=3k~si~c=4k. \\ \\ a= \sqrt{b^2+c^2} = \sqrt{25k^2}=5k. \\ \\ sin(x)= \frac{b}{a}= \frac{3k}{5k}= \frac{3}{5}.$