Question

Qual é o valor numérico da expressão cos(180° - x) + sen(x - 90°)?

PS: x = 60°

Answer 1

60 = π/3
180° = π
90° = π/2

sen (π/3 - π/2) + cos (π - π/3)

Formula da Adição Algebrica:

sen (π/3 - π/2) = sen π/3 cos π/2 - sen π/2 cos π/3
sen (- π/6) = √3/2 . 0 - 1 . 1/2
sen (- π/6) = - 1/2

cos (π - π/3) = cos π cos π/3 + sen π sen π/3
cos (2π/3) = - 1 . 1/2 + 0 . √3/3
cos (2π/3) = - 1/2 

Temos:

sen ( π/3 - π/2) + cos (π - π/3)
sen (- π/6) + cos (2π/3) = - 1/2 + ( - 1/2) = - 1/2 - 1/2 = - 1