Diket cos a 4/5 dan sin b 5/13 dengan sudut a dan b lancip. Nilai tan a+b adalah

Mapel : Matematika
Kelas : X SMA
Bab : Trigonometri

Pembahasan :
Ingat Cos x = Samping/Miring
Sin x = Depan/Miring
Tan x = Depan/Samping

Cos a = 4/5
Samping = 4
Miring = 5
Depan = √(5² - 4²) = √9 = 3

Tan a = 3/4

Sin b = 5/13
Depan = 5
Miring = 13
Samping = √(13² - 5²) = √144 = 12

Tan b = 5/12

Nilai Tan (a + b)
= (tan a + tan b)/(1 + tanAtanB)
= (3/4 + 5/12)/[1 + (3/4)(5/12)]
= (14/12)/(1 + 5/16)
= (7/6)/(21/16)
= (7 x 16)/(6 x 21)
= 112/126
= 56/63
= 8/9