Rumus-rumus Dalam Trigonometri

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Red-Mercenary - Trigonometri berasal dari bahasa Yunani, yakni Trigonos yang memiliki arti segitiga dan metron yang berarti ukuran. Berikut ini adalah beberapa rumus-rumus dalam Trigonometri dalam matematika.

1. Rumus Trigonometri untuk sudut rangkap
$sin 2\alpha =2 sin\alpha cos\alpha$
$cos 2\alpha =cos^{2}\alpha - sin^{2}\alpha$
$=2 cos^{2}\alpha - 1$
$=1- 2 sin^{2}\alpha$
$tan 2\alpha =\frac{2 tan\alpha }{1-tan^{2}\alpha }$
$cos 3 \alpha = 4 cos^{3}\alpha - 3 cos\alpha$
$sin 3 \alpha = 3 sin\alpha - 4 sin^{3}\alpha$

2. Rumus Trigonometri jumlah dan selisih dua sudut

$sin (\alpha +\beta )=sin\alpha cos\beta +cos\alpha sin\beta$
$sin (\alpha -\beta )=sin\alpha cos\beta -cos\alpha sin\beta$
$cos (\alpha +\beta )=cos\alpha cos\beta -sin\alpha sin\beta$
$cos (\alpha -\beta )=cos\alpha cos\beta +sin\alpha sin\beta$
$tan (\alpha +\beta )=\frac{tan\alpha +tan\beta }{1-tan\alpha tan\beta }$
$tan (\alpha -\beta )=\frac{tan\alpha -tan\beta }{1+tan\alpha tan\beta }$

3. Rumus penjumlahan dan pengurangan sinus serta cosinus
$cos\alpha +cos\beta =2cos\frac{1}{2}(\alpha +\beta )cos\frac{1}{2}(\alpha -\beta )$
$cos\alpha -cos\beta =-2sin\frac{1}{2}(\alpha +\beta )sin\frac{1}{2}(\alpha -\beta )$
$sin\alpha -sin\beta =2cos\frac{1}{2}(\alpha +\beta )sin\frac{1}{2}(\alpha -\beta )$
$sin\alpha +sin\beta =2sin\frac{1}{2}(\alpha +\beta )cos\frac{1}{2}(\alpha -\beta )$

4. Rumus perkalian sinus dan cosinus

$cos\alpha sin\beta =\frac{1}{2}(sin(\alpha +\beta )-sin(\alpha -\beta ))$
$sin\alpha cos\beta =\frac{1}{2}(sin(\alpha +\beta )+sin(\alpha -\beta ))$
$cos\alpha cos\beta =\frac{1}{2}(cos(\alpha +\beta )+cos(\alpha -\beta ))$
$sin\alpha sin\beta =-\frac{1}{2}(cos(\alpha +\beta )-cos(\alpha -\beta ))$

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