Tentukan nilai sin 2b, cos 2b, dan tan 2b, jika diketahui : 1. Tan B = 15/8 dan 180° < B < 270°

Bab Trigonometri
Matematika SMA Kelas X

180° < b < 270° → di kuadran III

tan b = 15/8 → y/x

r = √(x² + y²)
r = √(8² + 15²)
r = √(64 + 225)
r = √(289)
r = 17

sin b = y/r = -15/17
cos b = x/r = -8/17

1] sin 2b = 2 . sin b . cos b
sin 2b = 2 . (-15/17) . (-8/17)
sin 2b = 240/289

2] cos 2b = 2 cos² b - 1
cos 2b = 2 . (-8/17)² - 1
cos 2b = 2 . (64/289) - 289/289
cos 2b = 128/289 - 289/289
cos 2b = -161/289

3] tan 2b = sin 2b / cos 2b
tan 2b = (240/289) / (-161/289)
tan 2b = -240/161