# What is the distance between (5 ,(7 pi)/6 ) and (3 , (- 7 pi )/8 )?

Aug 13, 2017

The distance between two points is $2.06$ unit.

#### Explanation:

First point conversion from polar coodinate to cartesian coordinate.

$r = 5 , \theta = \frac{7 \cdot \pi}{6} = 3.6652$ ,

x -cordinate is $r \cdot \cos \theta = 5 \cdot \cos \left(3.6652\right) \approx - 4.33$

y -cordinate is $r \cdot \sin \theta = 5 \cdot \sin \left(3.6652\right) \approx - 2.5$

Second point from polar coodinate to cartesian coordinate.

$r = 3 , \theta = 2 \pi - \frac{- 7 \cdot \pi}{8} = 3.5343$ ,

x -cordinate is $r \cdot \cos \theta = 3 \cdot \cos \left(3.5343\right) \approx - 2.77$

y -cordinate is $r \cdot \sin \theta = 3 \cdot \sin \left(3.5343\right) \approx - 1.15$

Cartesian cordinates of two points are $\left(- 4.33 , - 2.5\right)$ and

 ( -2.77 , -1.15) . The distance between them is

$D = \sqrt{{\left({x}_{1} - {x}_{2}\right)}^{2} + {\left({y}_{1} - {y}_{2}\right)}^{2}}$ or

D= sqrt ((-4.33-(-2.77)^2+ (-2.5-(-1.15)^2) # or

$D \approx 2.06$ unit [Ans]