Rumus Dasar Trigonometri Yang Harus Kau Pahami
Cara Cepat Pintar Fisika - Rangkuman rumus dasar trigonometri yang harus kau pahami alasannya yakni rumus-rumus ini dipakai dalam aneka macam soal sebagainya.
Perhatikan segitiga Siku-siku berikut: 
Pada segitiga tersebut berlaku persamaan trigonometri sebagai berikut:$\small \\\sin A =\frac {a} {c}\\\small \cos A =\frac{b} {c}\\\small \tan A =\frac {a}{b} \\\small \csc A =\frac{1}{\sin A }=\frac{c}{a} \\\small \sec A =\frac{1}{\cos \alpha }=\frac{c}{B} \\\small \cot A =\frac{1}{\tan \alpha }=\frac{b}{a} $
$\small \\\tan \alpha = \frac{\sin \alpha }{\cos \alpha}\\\cot \alpha = \frac{1}{\tan \alpha}=\frac {\cos \alpha}{\sin \alpha}\\\sec \alpha =\frac {1}{\cos \alpha}\\\csc \alpha =\frac{1}{\sin \alpha}\\\sin ^2\alpha+\cos^2\alpha=1\\\tan ^2 \alpha +1=\sec^2 \alpha\\\cot^2\alpha+1=\csc^2\alpha$
$\small \sin {(\alpha +\beta )}=\sin \alpha \cos \beta + \cos \alpha \sin \beta\\\small \sin {(\alpha -\beta )}=\sin \alpha \cos \beta - \cos \alpha \sin \beta\\\small cos {(\alpha +\beta )}=\cos \alpha \cos \beta -\sin \alpha \sin \beta\\\small \cos {(\alpha -\beta )}=\cos \alpha \cos \beta + \sin \alpha \sin \beta\\\small \tan (\alpha +\beta )=\frac{\tan \alpha + \tan \beta}{1-\tan \alpha \tan \beta}\\\small \tan (\alpha -\beta )=\frac{\tan \alpha -\tan \beta}{1+\tan \alpha \tan \beta}$
$\small \\\sin 2\alpha =2 \sin \alpha \cos \alpha\\ \cos 2\alpha =\cos^2\alpha -\sin^2 \alpha\\\cos 2\alpha =2\cos^2\alpha -1\\\cos 2\alpha =1-2\sin^2\alpha \\\\ \tan 2\alpha =\frac{2\tan \alpha}{1-\tan^2 \alpha}\\\\\tan 2\alpha =\frac{2\cot \alpha }{\cot^2 \alpha -1}\\\\\tan 2\alpha =\frac{2}{\cot \alpha -\tan \alpha }$
$\small \sin{3\alpha }=3\sin \alpha -4\sin^3 \alpha \\\small \cos{3\alpha }=4\cos^3 \alpha -3\cos \alpha $
$\small \sin{\frac{1}{2}\alpha }=\pm\sqrt{\frac{1-\cos \alpha }{2}}\\\small \cos{\frac{1}{2}\alpha }=\pm\sqrt{\frac{1+\cos \alpha }{2}}\\\small \begin{align*}\tan{\frac{1}{2}\alpha }&=\pm\sqrt{\frac{1-\cos \alpha }{1+\cos \alpha }}\\&=\frac{\sin \alpha }{1+\cos \alpha }\\&=\frac{1-\cos \alpha }{\sin \alpha }\end{align*}$
$\small \sin \alpha +\sin \beta=2\sin \frac{1}{2}(\alpha +\beta )\cos \frac{1}{2}(\alpha -\beta )\\\small \sin \alpha-\sin \beta=2\cos \frac{1}{2}(\alpha +\beta )\sin \frac{1}{2}(\alpha -\beta )\\\small \cos \alpha+\cos \beta=2\cos \frac{1}{2}(\alpha +\beta )\cos \frac{1}{2}(\alpha -\beta )\\\small \cos \alpha-\cos \beta=-2\sin \frac{1}{2}(\alpha +\beta )\sin \frac{1}{2}(\alpha -\beta )$
$\small 2\sin \alpha \cos \alpha =\sin{(\alpha +\beta )}+\sin{(\alpha -\beta )}\\\small 2\cos \alpha \sin\beta =\sin{(\alpha +\beta )}-\sin{(\alpha -\beta )}\\\small 2\cos \alpha \cos\beta =\cos{(\alpha +\beta )}+\cos{(\alpha -\beta )}\\\small -2\sin \alpha \sin\beta =\cos{(\alpha +\beta )}-\cos{(\alpha -\beta )}$
Semoga bermanfaat Sumber http://carafisika.blogspot.com
Perhatikan segitiga Siku-siku berikut:
Identitas Trigonomteri
$\small \\\tan \alpha = \frac{\sin \alpha }{\cos \alpha}\\\cot \alpha = \frac{1}{\tan \alpha}=\frac {\cos \alpha}{\sin \alpha}\\\sec \alpha =\frac {1}{\cos \alpha}\\\csc \alpha =\frac{1}{\sin \alpha}\\\sin ^2\alpha+\cos^2\alpha=1\\\tan ^2 \alpha +1=\sec^2 \alpha\\\cot^2\alpha+1=\csc^2\alpha$
Trigonometri penjumlahan dan pengurangan:
$\small \sin {(\alpha +\beta )}=\sin \alpha \cos \beta + \cos \alpha \sin \beta\\\small \sin {(\alpha -\beta )}=\sin \alpha \cos \beta - \cos \alpha \sin \beta\\\small cos {(\alpha +\beta )}=\cos \alpha \cos \beta -\sin \alpha \sin \beta\\\small \cos {(\alpha -\beta )}=\cos \alpha \cos \beta + \sin \alpha \sin \beta\\\small \tan (\alpha +\beta )=\frac{\tan \alpha + \tan \beta}{1-\tan \alpha \tan \beta}\\\small \tan (\alpha -\beta )=\frac{\tan \alpha -\tan \beta}{1+\tan \alpha \tan \beta}$
Trigonometri Sudut Rangkap Dua:
$\small \\\sin 2\alpha =2 \sin \alpha \cos \alpha\\ \cos 2\alpha =\cos^2\alpha -\sin^2 \alpha\\\cos 2\alpha =2\cos^2\alpha -1\\\cos 2\alpha =1-2\sin^2\alpha \\\\ \tan 2\alpha =\frac{2\tan \alpha}{1-\tan^2 \alpha}\\\\\tan 2\alpha =\frac{2\cot \alpha }{\cot^2 \alpha -1}\\\\\tan 2\alpha =\frac{2}{\cot \alpha -\tan \alpha }$
Trigonometri Sudut Rangkap Tiga:
$\small \sin{3\alpha }=3\sin \alpha -4\sin^3 \alpha \\\small \cos{3\alpha }=4\cos^3 \alpha -3\cos \alpha $
Rumus trigonometri setengah sudut:
$\small \sin{\frac{1}{2}\alpha }=\pm\sqrt{\frac{1-\cos \alpha }{2}}\\\small \cos{\frac{1}{2}\alpha }=\pm\sqrt{\frac{1+\cos \alpha }{2}}\\\small \begin{align*}\tan{\frac{1}{2}\alpha }&=\pm\sqrt{\frac{1-\cos \alpha }{1+\cos \alpha }}\\&=\frac{\sin \alpha }{1+\cos \alpha }\\&=\frac{1-\cos \alpha }{\sin \alpha }\end{align*}$
Rumus Penjumlahan Trigonometri :
$\small \sin \alpha +\sin \beta=2\sin \frac{1}{2}(\alpha +\beta )\cos \frac{1}{2}(\alpha -\beta )\\\small \sin \alpha-\sin \beta=2\cos \frac{1}{2}(\alpha +\beta )\sin \frac{1}{2}(\alpha -\beta )\\\small \cos \alpha+\cos \beta=2\cos \frac{1}{2}(\alpha +\beta )\cos \frac{1}{2}(\alpha -\beta )\\\small \cos \alpha-\cos \beta=-2\sin \frac{1}{2}(\alpha +\beta )\sin \frac{1}{2}(\alpha -\beta )$
Rumus Perkalian Trigonometri:
$\small 2\sin \alpha \cos \alpha =\sin{(\alpha +\beta )}+\sin{(\alpha -\beta )}\\\small 2\cos \alpha \sin\beta =\sin{(\alpha +\beta )}-\sin{(\alpha -\beta )}\\\small 2\cos \alpha \cos\beta =\cos{(\alpha +\beta )}+\cos{(\alpha -\beta )}\\\small -2\sin \alpha \sin\beta =\cos{(\alpha +\beta )}-\cos{(\alpha -\beta )}$
Semoga bermanfaat Sumber http://carafisika.blogspot.com
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