Question

A.nilai dari sin 240 adalah?

Answer 1

Kategori Soal : Matematika - Trigonometri
Kelas : X (1 SMA)
Pembahasan :
Perbandingan 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

sin 30° = 1/2, cos 30° = 1/2 √3, tan 30° = 1/3 √3
sin 45° = 1/2 √2, cos 45° = 1/2 √2, tan 45° = 1
sin 60° = 1/2 √3, cos 60° = 1/2, tan 60° = √3
sin 90° = 1, cos 90° = 0, tan 90° = ∞

Mari kita lihat soal berikut.
sin 240° = sin (3 x 90 - 30)° = sin (270 - 30)° = -cos 30° = -1/2 √3.

Semangat!