Question

Sen x= 2/3, calcule o valor de tan² x .

Me ajudem por favor

Answer 1

Resposta:

sen(x)=2/3

sen²(x)+cos²(x)=1

cos²(x)=1-(2/3)²

cos²(x)=1-4/9

cos²(x)=5/9

ta²(x)=sen²(x)/cos²(x)

= (2/3)²/(5/9)

=(4/9)/(25/9)

=4/25

Answer 2

$\displaystyle \sf sen\ x=\frac{2}{3} \ \ ; \ \ tan^2x=\ ? \\\\ Sabemos \ que\ : \\\\ tan^2x=\frac{sen^2x}{cos^2x}\\\\ Rela{\c c}{\~a}o \ Fundamental\ da\ trigonometria : \\\\ sen^2x+cos^2x = 1 \\\\ cos^2x=1-sen^2x \\\\ Da{\'i}} : \\\\ tan^2x=\frac{sen^2x}{1-sen^2x } \\\\\\ tan^2x=\frac{\left(\frac{2}{3}\right)^2}{1-\left(\frac{2}{3}\right)^2} \\\\\\ tan^2x=\frac{\frac{4}{9}}{1-\frac{4}{9}} \to tan^2=\frac{\frac{4}{9}}{\frac{9-4}{9}} \\\\\\ \boxed{\sf tan^2x = \frac{4}{5} }\checkmark$