Diketahui cos a =3/5 dan cos b = 1/3 dengan a dan b sudut lancip. Tentukan nilai sin (a+b)

Materi : Trigonometri

Pembahasan :
Cos A = 3/5
Sin A = 4/5

Cos B = 1/3
Sin B = (2√2)/3

Maka...
Sin (A + B)
= Sin A Cos B + Cos A Sin B
= (4/5)(1/3) + (3/5)(2√2 / 3)
= 4/15 + (6√2)/15
= (6√2 + 4)/15

cos a =3/5 dan cos b = 1/3
Sin a =akar( 1- cos^2a)
=akar ( 1-9/25)
=akar( 25-9)/25
=akar 16/25
=4/5
Sin b =akar( 1- cos^2b)
=akar ( 1-1/9)
=akar( 9-1)/9
=akar 8/9
=2akar2/3
Maka... Sin (A + B) = Sin A Cos B + Cos A Sin B = (4/5)(1/3) + (3/5)(2(akar2)/ 3) = 4/15 + (6(akar2))/15 = (6(akar2)+ 4)/15