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SMK Teknologi dan Rekayasa

Soal 93 Rumus Trigonometri Jumlah-Selisih Sudut


Diketahui\ \ sin\ A=\frac{7}{25}\ \ dan\ \ cos\ B=\frac{5}{13}\ \ \ (A\ dan\ B\ sudut\ lancip).\\\\Nilai\ sin\ (A-B)\ adalah\ ....\\\\a.\ -\frac{232}{325}\ \ \ \ \ \ \ \ \ \ b.\ -\frac{253}{325}\ \ \ \ \ \ \ \ \ \ c.\ -\frac{235}{325}\\\\d.\ \ \frac{253}{325}\ \ \ \ \ \ \ \ \ \ \ \ \ e.\ \ \frac{323}{325}
Jawaban: b

Dengan\ menggunakan\ dalil\ Pythagoras,\ kita\ bisa\ mengingat\\tripel\ bilangan\ Pythagoras:\\\begin{matrix} & & & & & & & & & \end{matrix}7,\ \mathbf{24},\ 25\begin{matrix} & & & & & & & & & \end{matrix}5,\ \mathbf{12},\ 13
sin\ A=\frac{7}{25}\begin{matrix} & \end{matrix}\to \begin{matrix} & \end{matrix}cos\ A=\frac{24}{25}
cos\ B=\frac{5}{13}\begin{matrix} & \end{matrix}\to \begin{matrix} & \end{matrix}sin\ B=\frac{12}{13}
\begin{array}{rcl}sin\ (A-B)&=&sin\ A\ cos\ B-cos\ A\ sin\ B\\\\&=&\frac{7}{25}\ \times \ \frac{5}{13}\ \ -\ \ \frac{24}{25}\ \times \ \frac{12}{13}\\\\&=&\frac{35}{325}\ \ -\ \ \frac{288}{325}\\\\&=&-\frac{253}{325}\end{array}

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2 thoughts on “Soal 93 Rumus Trigonometri Jumlah-Selisih Sudut

  1. menyenangkan

    Posted by Reski | 24 Agustus 2012, 12:19 PM

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