Question

O conjunto imagem da função tangente é igual ao conjunto dos números reais. Determine tgx sabendo 3π/4 < x < 2π que e senx = -3/5 *
a)2/3
b)-3/4
c)√3/2
d)-1/2

Answer 1

$\large\boxed{\begin{array}{l}\sf sen(x)=-\dfrac{3}{5}\implies sen^2(x)=\dfrac{9}{25}\\\sf cos^2(x)=\dfrac{25}{25}-\dfrac{9}{25}\\\sf cos^2(x)=\dfrac{16}{25}\\\sf cos(x)=\sqrt{\dfrac{16}{25}}\\\sf cos(x)=\dfrac{4}{5}\\\sf tg(x)=\dfrac{sen(x)}{cos(x)}\\\sf tg(x)=\dfrac{-\frac{3}{\backslash\!\!\!5}}{\frac{4}{\backslash\!\!\!5}}\\\sf tg(x)=-\dfrac{3}{4}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~b}}}}\end{array}}$