MCQ
Convert $\Big(8, \frac{2\pi}{3}\Big)$ into Argand plane representation:
- ✓$(\text{-4, } 4\sqrt{3})$
- B$(\text{4, } 4\sqrt{3})$
- C$(\text{4} \sqrt{\text{3, }}4)$
- D$(\text{-4} \sqrt{\text{3, }}4)$
✓
Answer
Correct option: A.
$(\text{-4, } 4\sqrt{3})$
To convert polar representation $(\text{r, }\theta)$ into argand plane $(\text{x, }\text{y}),$ substitute $\text{x}=\text{r}\cos\theta$ and $\text{y}=\text{r}\sin\theta$
$\text{x}=8\cos\frac{2\pi}{3}=8\cos\Big(\frac{\pi-\pi}{3}\Big)=8\Big(\frac{-1}{2}\Big)=-4$
$\text{y}=8\cos\frac{2\pi}{3}=8\cos\Big(\frac{\pi-\pi}{3}\Big)=8\Big(\frac{\sqrt{3}}{2}\Big)=4\sqrt{3}$
$\text{x}=8\cos\frac{2\pi}{3}=8\cos\Big(\frac{\pi-\pi}{3}\Big)=8\Big(\frac{-1}{2}\Big)=-4$
$\text{y}=8\cos\frac{2\pi}{3}=8\cos\Big(\frac{\pi-\pi}{3}\Big)=8\Big(\frac{\sqrt{3}}{2}\Big)=4\sqrt{3}$
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