Jika tan x=1/2 dan 0
Matematika
ardiana991
Pertanyaan
Jika tan x=1/2 dan 0<x<π/2, maka nilai dari 3cosx + sin(x-π/2) + cos(π-x) =...
1 Jawaban
-
1. Jawaban DB45
Triginometri
tan x = 1/2 , dan x di kuadran 1
sin x = 1/ √(1²+2²) = 1/√5 = 1/5 √5
cos x = 2/√(1²+2²) = 2/√5 = 2/5 √5
.
3 cos x + sin (x - π/2) + cos (π -x) =
= 3 cos x + sin {-(π/2 - x)} + cos(π -x)
= 3 cos x - sin (π/2 - x) + cos (π - x)
= 3 cos x - cos x - sin x
= 2 cos x - sin x
= 2 (2/5 √5) - 1/5 √5
= (4/5 - 1/5) √5
= 3/5 √5