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SMK Teknologi dan Rekayasa

Soal 91 Koordinat Kutub – Koordinat Kartesius


Jika\ diketahui\ koordinat\ kutub\ (6\sqrt{3},\ 60^{\circ}),\ maka\ koordinat\\kartesiusnya\ adalah\ ....\\a.\ \ (3,\ 3)\ \ \ \ \ \ \ \ \ \ \ \ \ \ b.\ \ (3,\ \sqrt{3})\ \ \ \ \ \ \ \ \ \ \ \ \ \ c.\ \ (3,\ 3\sqrt{3})\\d.\ \ (3\sqrt{3},\ 9)\ \ \ \ \ \ \ \ \ \ e.\ \ (9,\ 3\sqrt{3})
Jawaban: d

\begin{array}{rcl}Koordinat\ kutub&\rightarrow &Koordinat\ kartesius\\(r,\ \alpha )&\rightarrow &(x,\ y)\end{array}
r=6\sqrt{3},\ \ \alpha =60^{\circ}\\(Karena\ \alpha \ sudut\ di\ kuadran\ I,\ maka\ x\ positif\ dan\ y\ positif)
\begin{array}{rcl}x&=&r\ cos\ \alpha\\&=&6\sqrt{3}\times cos\ 60^{\circ}\\&=&6\sqrt{3}\times \frac{1}{2}\\&=&3\sqrt{3}\end{array}
\begin{array}{rcl}y&=&r\ sin\ \alpha \\&=&6\sqrt{3}\times sin\ 60^{\circ}\\&=&6\sqrt{3}\times \ \frac{1}{2}\sqrt{3}\\&=&3\times 3\\&=&9\end{array}
Koordinat\ kartesiusnya\ adalah\ (3\sqrt{3},\ 9)

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