Question

Calcule senB, cosB e determine o valor de cos2B + sen2B.

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{sen\:\Theta = \dfrac{cateto\:oposto}{hipotenusa}}$

$\mathsf{sen\:B = \dfrac{4}{4\sqrt{2}}}$

$\mathsf{sen\:B = \dfrac{1}{\sqrt{2}}}$

$\mathsf{sen\:B = \dfrac{\sqrt{2}}{2}}$

$\mathsf{cos\:\Theta = \dfrac{cateto\:adjacente}{hipotenusa}}$

$\mathsf{cos\:B = \dfrac{4}{4\sqrt{2}}}$

$\mathsf{cos\:B = \dfrac{1}{\sqrt{2}}}$

$\mathsf{cos\:B = \dfrac{\sqrt{2}}{2}}$

$\mathsf{cos^2\:B + sen^2\:B = \left(\dfrac{\sqrt{2}}{2}\right)^2 + \left(\dfrac{\sqrt{2}}{2}\right)^2}$

$\mathsf{cos^2\:B + sen^2\:B = \left(\dfrac{2}{4}\right) + \left(\dfrac{2}{4}\right)}$

$\mathsf{cos^2\:B + sen^2\:B = \left(\dfrac{4}{4}\right)}$

$\boxed{\boxed{\mathsf{cos^2\:B + sen^2\:B = 1}}}$