Question

The Cartesian coordinates of the point $(3,\frac{\pi }{3})$ are :

• A. $(3,3\sqrt{3})$
• B. $(\frac{3}{2},\frac{3\sqrt{3}}{2})$
• C. $(\sqrt{2},\frac{5}{4})$
• D. $(2,\sqrt{3})$

Answer 1

Answer: (B)

$(\frac{3}{2},\frac{3\sqrt{3}}{2})$

Given Polar coordinates are $(r,\theta )=(3,\frac{\pi }{3})$

Polar coordinates to Cartesian coordinates
i.e. $(r,\theta )\Rightarrow (x,y)$

As we know, $x=r\cos \theta$ and $y=r\sin \theta$
$(x,y)\Rightarrow \left(r\cos \right(\theta ),r\sin (\theta \left)\right)$
$\Rightarrow (x,y)=(3\cos \frac{\pi }{3},3\sin \frac{\pi }{3})$
$\Rightarrow (x,y)=(3\times \frac{1}{2},3\times \frac{\sqrt{3}}{2})$
$\Rightarrow (x,y)=(\frac{3}{2},\frac{3\sqrt{3}}{2})$