Question

dado que sem alfa=4/5 e pi/2 < alfa < pi, calcular o valor de cos alfa.​

Answer 1

Explicação passo-a-passo:

Equação trigonometrica:

$\mathsf{\sin^2(\alpha)+\cos^2(\alpha)~=~1 }$

$\mathsf{\cos^2(\alpha)~=~1-\sin^2(\alpha) }$

$\mathsf{\cos^2(\alpha)~=~1-\Big(\dfrac{4}{5}\Big)^2 }$

$\mathsf{\cos^2(\alpha)~=~1-\dfrac{16}{25} }$

$\mathsf{\cos^2(\alpha)~=~\dfrac{9}{25} }$

$\mathsf{\cos(\alpha)~=~\pm\sqrt{\dfrac{9}{25}} }$

$\mathsf{\cos(\alpha)~=~\pm\dfrac{3}{5} }$

Como:

$\mathsf{\dfrac{π}{2}<\alpha<π }$

Então:

$\boxed{\mathsf{\cos(\alpha)~=~-\dfrac{3}{5} }}}}$

Espero ter ajudado bastante!)