Jawaban:

Kelas : X (1 SMA)

Materi : Trigonometri

Kata Kunci : trigonomteri, pembagian, sudut

Pembahasan :

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

Kuadran I : 0° < α < 90° (0 < α < \frac{ \pi }{2}

2

π

)

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° ( \frac{ \pi }{2}

2

π

< 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 < \frac{3\pi }{2}

2

3π

)

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° ( \frac{3\pi }{2}

2

3π

< 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 tersebut.

Tentukan nilai dari sin 110°!

Jawab :

sin 110°

= sin (180 - 70)°

= sin 70°

= sin (90 - 20)°

= cos 20°

Jadi, nilai dari sin 110° sama dengan sin 70° atau cos 20°.