Question

$\alpha ( \frac{\pi}{2} si\pi) \: asa \: incat \: \sin( \alpha ) = \frac{3}{5} \: calculati \: \tan( \alpha )$

Answer 1

Răspuns

-3/4

Explicație pas cu pas:

Folosim teorema fundamentala a trigonometriei.

sin²α+cos²α=1

cos²α=1-sin²α

cos²α=1-9/25

cos²α=16/25

cos α=± 4/5

Dar mai stim ca α∈(π/2 , π) ,adica cadranul 2 ,unde cosinusul e negativ, ceea ce inseamna ca cos α=-4/5

tg α =sin α/cos α = 3/5 / -4/5= -3/4

Answer 2

$\it a\in\left(\dfrac{\pi}{2},\ \pi\right) \Rightarrow cosa<0\\ \\ cosa=-\sqrt{1-sin^2a}=-\sqrt{1-\dfrac{9}{25}}=-\sqrt{\dfrac{16}{25}}=-\dfrac{4}{5}\\ \\ tga=\dfrac{sina}{cosa}=\dfrac{\dfrac{3}{5}}{-\dfrac{4}{5}}=-\dfrac{3}{4}$