Nyatakan dengan perbandingan trigonometri sudut lancip!

Jawaban:

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.

1. sin 250° = -cos (3 x 90 – 20)° = -cos 20°

2. cos 320° = cos (4 x 90 – 40)° = cos 40°

3. tan 160° = -tan (2 x 90 – 20)° = -tan 20°

4. cotan 130° = -cotan (2 x 90 – 50)° = -cotan 50°

5. sec 273° = sec (4 x 90 – 87)° = sec 87°

6. cosec 350° = -cosec (4 x 90 – 10)° = -cosec 10°