a.sin a= 4/5,cos β=5/13, a dan β di kuadran 1
b.sin a=2/3,cos β=3/4, a di kuadran 2dan 4
Carilah nilai sin (a+β),cos (a-β),dan tan (a-β) jika diketahui:
Kuadran 1 (semua positif)
sin α = 4/5, (de = 4, mi = 5, sa = 3) cos α= 3/5, tan α = 4/3
cos β = 5/13, (sa = 5, mi = 13, de = 12) sin β= 12/13, tan β = 12/5
sin (α + β) = sin α cos β + cos α sin β
sin (α + β) = (4/5)(5/13) + (3/5)(12/13) = 56/65
cos (α - β) = cos α cos β + sin α sin β
cos (α - β) = (3/5)(5/13) + (4/5)(12/13) = 63/65
tan (α - β) = (tan α – tan β)/(1 – tan α tan β)
tan (α - β) = ([4/3] – [12/5])/(1 – [4/3][12/5]) = …
kuadran II (sin positif, cos negatif, tan negatif)
kuadran III (sin negatif, cos negatif, tan positif)
kuadran IV (sin negatif, cos positif, tan negatif)