Question

Consulte a tabela trigonométrica e, aplicando as relações de simetria, anote no caderno o valor de: A) sen 140°B sen 255°C) sen 310°

Answer 1

Olá

Podemos aplicar a regra:

$\sin x =\sin(180^{\circ}-x)$

Então, use-a na letras A, B e C

Lembre-se que

$\sin x =\sin (-(180^{\circ}-x))=\sin (x-180^{\circ})~|~ x>180^{\circ}$

$\mathtt{\sin 140^{\circ}=\sen(180^{\circ}-140^{\circ})=\sin 40^{\circ}}\\\\\\ \mathtt{\sin 255^{\circ}=\sin (255^{\circ}-180^{\circ})=\sin 75^{\circ}}\\\\\\ \mathtt{\sin 310^{\circ}=\sin (310^{\circ}-180^{\circ})=\sin130^{\circ}=\sin (180^{\circ}-130^{\circ}) =\sin 50^{\circ}}$

Respostas
$\begin{cases} A = \sin 40^{\circ}\\ B = \sin 75^{\circ}\\ C =\sin 50^{\circ}\\ \end{cases}$