Cos alpha = 1/3√6 dan tan beta = 1/3.alpha dan beta sudut lancip,nilai sin (alpha + beta)=

Materi : Trigonometri

Pembahasan :
Cos α = Samping/Miring
Cos α = 1/3 √6

Samping = √6
Miring = 3
Depan = √[3² - (√6)²] = √3

Sin α = Depan/Miring
Sin α = 1/3 √3

Tan β = Depan/Samping
Tan β = 1/3

Depan = 1
Samping = 3
Miring = √[3² + 1²] = √10

Sin β = Depan/Miring = 1/10 √10
Cos β = Samping/Miring = 3/10 √10

Maka...
Sin (α + β)
= Sin α . Cos β + Cos α Sin β
= (1/3 √3)(3/10 √10) + (1/3 √6)(1/10 √10)
= 1/10 √30 + 1/30 √60
= 1/10 √30 + 1/30 . 2√15
= 1/10 √30 + 1/15 √15
= 1/5 (1/2 √30 + 1/3 √15)