Question

me ajudeem,por favorr​

Answer 1

Resposta:

$sen\alpha$=$\frac{4}{5}$

Explicação passo a passo:

1º

$cos\alpha$=$\frac{3}{5}$

$cotg\alpha$=$\frac{3}{4}$

$tg\alpha$=$\frac{sen\alpha}{cos\alpha}$

pelos valores so pode ser referente ao triangulo 5x4x3

mas pela formula a cotangente= 1/tangente

ou seja;

$\frac{3}{4}$=$\frac{1}{tg\alpha }$

3.$tg\alpha$=4

substitundo a tangente

3$\frac{sen\alpha}{cos\alpha}$=4

$sen\alpha$=$\frac{4}{3}$.$cos\alpha$

$sen\alpha$=$\frac{4}{3}$.$\frac{3}{5}$

$sen\alpha$=$\frac{4}{5}$

2.

2a) sec 300° = $\frac{1}{sen 300°}$

sen 300° = - sen 60° = - $\frac{\sqrt{3}}{2}$

sec 300° = $\frac{1}{-\frac{\sqrt{3}}{2}}$

sec 300° = .$\frac{1}{-\frac{\sqrt{3}}{2}}.\frac{-\frac{\sqrt{3}}{2}}{-\frac{\sqrt{3}}{2}}$

sec 300° = .$\frac{-\frac{\sqrt{3}}{2}}{\frac{3}{4}}.$

sec 300° = .$-\frac{4\sqrt{3}}{6}$

sec 300° = .$-\frac{2\sqrt{3}}{3}$

2b)

π=180°

$cossec\frac{8.180}{3}$

$cossec=\frac{1}{cos\frac{8.180}{3} }$

$cossec=\frac{1}{cos480}$

cos 480 = cos 120 = - cos 60

cos 60 =$\frac{1}{2}$

cossec 480° = $\frac{1}{\frac{-1}{2} }$

cossec 480° = -2