Trigonometri 2

TRIGONOMETRI

 

A. JUMLAH DAN SELISIH SUDUT
No Rumus
1 \(\sin (A + B) = \sin A \cos B + \cos A \sin B \)

\(\sin (A - B) = \sin A \cos B - \cos A \sin B \)

2 \(\cos (A + B) = \cos A \cos B - \sin A \sin B \)

\(\cos (A - B) = \cos A \cos B + \sin A \sin B \)

3 \(\tan (A + B) = \dfrac{\tan A + \tan B}{1 - \tan A \tan B} \)

 

\(\tan (A - B) = \dfrac{\tan A - \tan B}{1 + \tan A \tan B} \)

B. SUDUT RANGKAP
No Rumus Rumus Rumus
1 \(\sin 2x = 2 \sin x \cos x  \) \(\sin 3x = 3 \sin x - 4 \sin^3 x  \)
2 \(\cos 2x = \cos^2 x - \sin^2 x \)

\(\cos 2x = 2\cos^2 x - 1 \)

\(\cos 2x = 1 - 2\sin^2 x \)

\(\cos^2 x = \dfrac{1}{2} + \dfrac{1}{2} \cos 2x \)

\(\sin^2 x = \dfrac{1}{2} - \dfrac{1}{2} \cos 2x \)

\(\cos 3x = 4\cos^3 x - 3 \cos x \)
3 \(\tan 2x = \dfrac{2 \tan x}{1 - \tan^2 x} \) \(\tan 3x = \dfrac{3 \tan x - \tan^3 x}{1 - 3 \tan^2 x}\)
C. PENJUMLAHAN DAN PERKALIAN FUNGSI
No Rumus Rumus
1 \(\sin A + \sin B = 2 \sin \frac{1}{2} (A + B) \cos \frac{1}{2} (A - B)\) \(2 \sin A \cos B = \sin (A + B) + \sin (A - B) \)
2 \(\sin A - \sin B = 2 \cos \frac{1}{2} (A + B) \sin \frac{1}{2} (A - B)\) \(2 \cos A \sin B = \sin (A + B) - \sin (A - B) \)
3 \(\cos A + \cos B = 2 \cos \frac{1}{2} (A + B) \cos \frac{1}{2} (A - B)\) \(2 \cos A \cos B = \cos (A + B) + \cos (A - B) \)
4 \(\cos A - \cos B = -2 \sin \frac{1}{2} (A + B) \sin \frac{1}{2} (A - B)\) \(-2 \sin A \sin B = \cos (A + B) - \cos (A - B) \)