Benang Lurus
Benang Lurus
Rumus Dasar Limit Trigonometri
Rumus dasar
(1) \(\lim\limits_{x \rightarrow 0} \dfrac{\sin px}{x} = p\)
(2) \(\lim\limits_{x \rightarrow 0} \dfrac{\tan qx}{x} = q\)
(3) \(\lim\limits_{x \rightarrow 0} \dfrac{\sin px}{\tan qx} = \dfrac{p}{q}\)
Rumus sudut rangkap trigonometri
(1) \(\sin^2 x + \cos^2 x = 1\)
(2) \(1 + \tan^2 x = \sec^2 x\)
(3) \(1 + \cot^2 x = \csc^2 x\)
Rumus sudut rangkap trigonometri
(1) \(\sin 2x = 2\sin x \cos x\)
(2) \(\cos 2x = 1 \:-\:2\sin^2 x\)
(3) \(\cos 2x = 2\cos^2 x \:-\: 1\)
(4) \(\cos 2x = \cos^2 x \:-\: \sin^2 x\)
Rumus jumlah fungsi trigonometri
(1) \(\sin x + \sin y = 2\sin \frac{1}{2} (x + y) \cos \frac{1}{2} (x \:-\: y)\)
(2) \(\sin x \:-\: \sin y = 2\cos \frac{1}{2} (x + y) \sin \frac{1}{2} (x \:-\: y)\)
(3) \(\cos x + \cos y = 2\cos \frac{1}{2} (x + y) \cos \frac{1}{2} (x \:-\: y)\)
(4) \(\cos x \:-\: \cos y = -2\sin \frac{1}{2} (x + y) \sin \frac{1}{2} (x \:-\: y)\)
Rumus limit eksponen
(1) \(\lim\limits_{x \rightarrow \infty} [1 + \text{f(x)}]^{\text{g(x)}} = e^{\lim\limits_{x \rightarrow \infty} \text{f(x)}\cdot \text{g(x)}}\)
(2) \(\lim\limits_{x \rightarrow 0} [1 + \text{f(x)}]^{\text{g(x)}} = e^{\lim\limits_{x \rightarrow 0} \text{f(x)}\cdot \text{g(x)}}\)