Question

Exercitiul 5 si 6 va rog frumos

Answer 1

5.  $\displaystyle\frac{BM}{BC}=\frac13\Rightarrow BM=\frac13BC$

$\displaystyle\overrightarrow{AM}=\overrightarrow{AB}+\overrightarrow{BM}=\overrightarrow{AB}+\frac13\overrightarrow{BC}=\overrightarrow{AB}+\frac13(\overrightarrow{BA}+\overrightarrow{AC})=\overrightarrow{AB}+\frac13(-\overrightarrow{AB}+\overrightarrow{AC})=\frac23\overrightarrow{AB}+\frac13\overrightarrow{AC}$

6.

$\displaystyle\alpha\in\left(\frac\pi2, \pi\right)\Rightarrow \cos x<0\\\sin^2x+\cos^x=1\Rightarrow \cos^2x=1-\sin^2x=\displaystyle\frac{16}{25}\Rightarrow|\cos x|=\frac{16}{25}\Rightarrow \cos x=-\frac45\\\\tg x=\displaystyle\frac{\sin x}{\cos x}=\frac{\frac35}{-\frac45}=-\frac34$