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SMK Teknologi dan Rekayasa

soal 96 Rumus Trigonometri Jumlah-Selisih Sudut


Nilai\ dari\ sin\ 15^{\circ}\ adalah\ ....\\\\a.\ \ \frac{1}{4}(\sqrt{6}-\sqrt{2})\ \ \ \ \ \ \ \ \ \ b.\ \ \frac{1}{4}(\sqrt{3}-\sqrt{2})\ \ \ \ \ \ \ \ \ \ c.\ \ \sqrt{6}-\sqrt{2}\\\\d.\ \ \frac{1}{4}(\sqrt{2}-\sqrt{3})\ \ \ \ \ \ \ \ \ \ e.\ \ \frac{1}{4}(\sqrt{2}-\sqrt{6})
Jawaban: a

sin\ (\alpha -\beta )=sin\ \alpha \ cos\ \beta -cos\ \alpha \ sin\ \beta
\begin{array}{rcl}sin\ 15^{\circ}&=&sin\ (45-30)^{\circ}\\\\&=&sin\ 45^{\circ}\ cos\ 30^{\circ}-cos\ 45^{\circ}\ sin 30^{\circ}\\\\&=&\frac{1}{2}\sqrt{2}\ \times \ \frac{1}{2}\sqrt{3}\ -\ \frac{1}{2}\sqrt{2}\ \times \ \frac{1}{2}\\\\&=&\frac{1}{4}\sqrt{6}\ -\ \frac{1}{4}\sqrt{2}\\\\&=&\frac{1}{4}(\sqrt{6}\ -\ \sqrt{2})\end{array}

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4 thoughts on “soal 96 Rumus Trigonometri Jumlah-Selisih Sudut

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    Posted by mala | 27 April 2012, 10:47 PM
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