Nilai dari sin 280° - sin 140° per cos 280° - cos 140° adalah?

Kelas: 11
Mapel: Matematika
Kategori: Trigonometri Lanjut
Kata kunci: trigonometri, sin, cos
Kode: 11.2.3 (Kelas 11 Matematika Bab 3-Trigonometri Lanjut)

rumus jumlah dan selisih sinus dan kosinus
sin A + sin B = 2 sin 1/2(A + B) cos 1/2 (A – B ) 
sin A – sin B = 2 cos 1/2(A + B) sin 1/2(A – B)
cos A + cos B = 2 cos 1/2(A + B) cos 1/2(A – B)
cos A – cos B = -2 sin 1/2(A + B) sin 1/2(A – B)

[tex] \frac{sin 280^{\circ}-sin 140^{\circ}}{cos280^{\circ}-cos140^{\circ}} \\ = \frac{2cos \frac{1}{2} (280^{\circ}+140^{\circ})sin \frac{1}{2} (280^{\circ}-140^{\circ})}{-2sin \frac{1}{2} (280^{\circ}+140^{\circ})sin \frac{1}{2} (280^{\circ}-140^{\circ})} \\ =- \frac{cos \frac{1}{2} (420^{\circ})}{sin \frac{1}{2} (420^{\circ})} \\ =-cotan210^{\circ} \\ =-cotan(180^{\circ}+30^{\circ}) \\ =-cotan30^{\circ} \\ =-\sqrt{3}[/tex]

Semangat belajar!
Semoga membantu :)