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SMK Teknologi dan Rekayasa

Soal 90 Koordinat Kutub – Koordinat Kartesius


Koordinat\ kutub\ titik\ (-4,\ 4)\ adalah\ ....\\a.\ \ (4\sqrt{2},\ 135^{\circ})\ \ \ \ \ \ \ \ \ \ b.\ \ (2\sqrt{2},\ 135^{\circ})\ \ \ \ \ \ \ \ \ \ c.\ \ (-2\sqrt{2},\ 45^{\circ})\\d.\ \ (-4\sqrt{2},\ 45^{\circ})\ \ \ \ \ \ \ \ \ e.\ \ (-2\sqrt{2},\ 135^{\circ})
Jawaban: a

\begin{array}{rcl}Koordinat\ kartesius&\rightarrow &Koordinat\ kutub\\(x,\ y)&\rightarrow &(r,\ \alpha )\end{array}
x=-4,\ \ y=4\\(Karena\ x\ negatif\ dan\ y\ positif,\ maka\ \alpha \ sudut\ di\ kuadran\ II)
\begin{array}{rcl}r&=&\sqrt{x^{2}+y^{2}}\\&=&\sqrt{(-4)^{2}+4^{2}}\\&=&\sqrt{16+16}\\&=&\sqrt{2.16}\\&=&\sqrt{2}\times \sqrt{16}\\&=&\sqrt{2}\times 4\\&=&4\sqrt{2}\end{array}
\begin{array}{rcl}tan\ \alpha &=&\frac{y}{x}\\\\&=&\frac{4}{-4}\\\\&=&-1\end{array}
Karena\ \alpha \ sudut\ di\ kuadran\ II,\ maka:\ \alpha =(180-45)^{\circ}=135^{\circ}
Koordinat\ kutubnya\ adalah\ (4\sqrt{2},\ 135^{\circ})

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