# What is the distance between the following polar coordinates?:  (1,pi/3), (-1,pi/2)

Nov 29, 2015

These are both on the unit circle.

#### Explanation:

Since $\frac{\pi}{2}$ is ${90}^{o}$, but the $- 1$ moves it ${180}^{o}$ from (0,1) to (0,-1)

The point $\left(- 1 , \frac{\pi}{2}\right)$ is at $\left(0 , - 1\right)$

$\frac{\pi}{3} = {60}^{o}$, therefore ...
$x = \cos 60 = \frac{1}{2}$ and $y = \sin 60 = \frac{\sqrt{3}}{2} \approx 0.8660$

So, the point $\left(1 , \frac{\pi}{3}\right)$ is at $\approx \left(\frac{1}{2} , 0.8660\right)$

Using the distance formula :

distance $= \sqrt{{\left(\frac{1}{2} - 0\right)}^{2} + {\left(\frac{\sqrt{3}}{2} + 1\right)}^{2}} = \sqrt{2 + \sqrt{3}} \approx 1.9$

hope that helped