Question

Se um ângulo do segundo quadrante tem cosseno igual a − 7/10 , calcule os valores de seu seno e de sua tangente. ​

Answer 1

$\large\boxed{\begin{array}{l}\rm cos(x)=-\dfrac{7}{10}\longrightarrow sec(x)=-\dfrac{10}{7}\\\\\rm tg^2(x)=sec^2(x)-1\\\rm tg^2(x)=\bigg(-\dfrac{10}{7}\bigg)^2-1\\\\\rm tg^2(x)=\dfrac{100}{49}-1\\\\\rm tg^2(x)=\dfrac{100-49}{49}\\\\\rm tg^2(x)=\dfrac{51}{49}\\\\\rm tg(x)=-\sqrt{\dfrac{51}{49}}\\\\\rm tg(x)=-\dfrac{\sqrt{51}}{7}\end{array}}$

$\large\boxed{\begin{array}{l}\rm sen(x)=cos(x)\cdot tg(x)\\\rm sen(x)=\bigg(\!\!\!\!-\dfrac{\backslash\!\!\!7}{10}\bigg)\cdot\bigg(\!\!\!-\dfrac{\sqrt{51}}{\backslash\!\!\!7}\bigg)\\\\\rm sen(x)=\dfrac{\sqrt{51}}{10}\end{array}}$