Question

Em uma circunferência trigonométrica:
Se E = sen 70° - cos 20° + sen 30° + sen 150° então:

A) 1
B) -1
C) 2
D) -2
E) 3

Answer 1

Seno e cosseno de arcos complementares

$\boxed{\boxed{\mathsf{\cos(x)=\sin(90^{\circ}-x)}}}$

$\boxed{\boxed{\mathsf{\sin(x)=\cos(90^{\circ}-x)}}}$

$\boxed{\boxed{\mathsf{\cos(20^{\circ}) =\sin(90^{\circ}-20^{\circ}) =\sin(70^{\circ})}}}$

$\boxed{\boxed{\mathsf{\sin(150^{\circ}) =\sin(180^{\circ}-150^{\circ})=\sin(30^{\circ})}}}$

substituindo os valores na expressão temos:

$\mathsf{E=\sin(70^{\circ})-\cos(20^{\circ})+\sin(30^{\circ})+\sin(150^{\circ})}\\\mathsf{E=\cancel{\sin(70^{\circ})}-\cancel{\sin(70^{\circ})} +\dfrac{1}{2}+\dfrac{1}{2}}$

$\boxed{\boxed{\mathsf{E=1}}}$

$\mathsf{Alternativa\:A}$