Jawaban:

Kategori Soal : Matematika - Trigonometri

Kelas : X (1 SMA)

Pembahasan :

Pembagian sudut dalam trigonometri.

Dalam trigonometri, besar sudut α dibagi menjadi 4 kelompok, yaitu :

Kuadran I : 0° < α < 90° (0 < α < π/2)

sin (90° - α) = cos α

cos (90° - α) = sin α

tan (90° - α) = cotan α

cotan (90° - α) = tan α

secan (90° - α) = sec α

sec (90° - α) = cosec α

Kuadran II : 90° < α < 180° (π/2 < α < π)

sin (180° - α) = sin α

cos (180° - α) = -cos α

tan (180° - α) = -tan α

cotan (180° - α) = -cotan α

secan (180° - α) = secan α

sec (180° - α) = -sec α

Kuadran III : 180° < α < 270° (π < α < 3π/2)

sin (270° - α) = -cos α

cos (270° - α) = -sin α

tan (270° - α) = cotan α

cotan (270° - α) = tan α

secan (270° - α) = -sec α

sec (270° - α) = -cosec α

Kuadran IV : 270° < α < 360° (3π/2 < α < 2π)

sin (360° - α) =sin (-α) = -sin α

cos (360° - α) = cos (-α) = cos α

tan (360° - α) = tan (-α) = -tan α

cotan (360° - α) = cotan (-α) = -cotan α

secan (360° - α) = secan (-α) = -secan α

sec (360° - α) sec (-α) = sec α

Mari kita lihat soal berikut. Sayang soal belum lengkap. Kemungkinan soal yang ditanyakan yaitu (cos 170° + cos 80°) : (sin 170° - sin 80°).

Diketahui

cos 170° = -cos (180 - 10)° = -cos 10°

cos 80° = sin (90 - 10)° = sin 10°

sin 170° = sin (180 - 10)° = sin 10°

sin 80° = cos (90 - 10)° = cos 10°

sehingga

(cos 170° + cos 80°) : (sin 170° - sin 80°)

= (-cos 10° + sin 10°) : (sin 10° - cos 10°)

= (-cos 10° + sin 10°) : (-cos 10° + sin 10°)

= 1