Question

Stiind ca a apartine (pi, 3pi/2) si sin a = -2/5 sa se calculeze cos a.​

Answer 1

Explicație pas cu pas:

FOLOSIM FORMULA FUNDAMENTALA A TRIGONOMETRIEI

sin²a + cos²a=1

$( - \frac{2}{5} ) {}^{2} + cos {}^{2}a = 1 \\ \\ \frac{4}{25} + cos {}^{2}a = {}^{25)} 1 \\ \\ cos {}^{2}a = \frac{25 - 4}{25} \\ \\ cos {}^{2}a = \frac{21}{25} \\ \\ cos \: a = \sqrt{ \frac{21}{25} } \\ \\ cos \: a = + - \frac{ \sqrt{21} }{5} \\ \\ a \: apartne \: cadranului \: 3 \\ \\ cos \: a = - \frac{ \sqrt{21} }{5}$

Answer 2

$\it a\in \Big(\pi,\ \dfrac{3\pi}{2}\Big) \Rightarrow cosa<0\\ \\ cosa=-\sqrt{1-sin^2a}=-\sqrt{1-\Big(-\dfrac{2}{5}\Big)^2}=-\sqrt{1-\dfrac{4}{25}}=-\sqrt{\dfrac{21}{25}}=-\dfrac{\sqrt{21}}5{}$