Question

Se cos x = 2/5 e x está no terceiro quadrante, calcule o valor de senx.

Answer 1

$\mathsf{cos(x)=-\dfrac{2}{5}\implies~cos^2(x)=(-\dfrac{2}{5})^2=\dfrac{4}{25}}$

$\mathsf{sen^2(x)=1-\dfrac{4}{25}=\dfrac{21}{25}}\\\mathsf{sen(x)=-\sqrt{\dfrac{21}{25}}}\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{sen(x)=-\dfrac{\sqrt{21}}{5}}}}}}$