What is the distance between $(5, \frac{7 π}{4})$ $(5 , (7 pi)/4 )$ and $(- 4, π)$ $(-4 , pi )$ ?

Question

What is the distance between $(5, \frac{7 π}{4})$ $(5 , (7 pi)/4 )$ and $(- 4, π)$ $(-4 , pi )$ ?

1 Answer

Impact of this question

2248 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-06T19:21:03

$3.56595$ $3.56595$ units

Explanation:

The distance formula for polar coordinates is

$d = \sqrt{r_{1}^{2} + r_{2}^{2} - 2 r_{1} r_{2} cos (θ_{1} - θ_{2})}$ $d=sqrt(r_1^2+r_2^2-2r_1r_2Cos(theta_1-theta_2)$
Where $d$ $d$ is the distance between the two points, $r_{1}$ $r_1$ , and $θ_{1}$ $theta_1$ are the polar coordinates of one point and $r_{2}$ $r_2$ and $θ_{2}$ $theta_2$ are the polar coordinates of another point.
Let $(r_{1}, θ_{1})$ $(r_1,theta_1)$ represent $(5, \frac{7 π}{4})$ $(5,(7pi)/4)$ and $(r_{2}, θ_{2})$ $(r_2,theta_2)$ represent $(- 4, π)$ $(-4,pi)$ .
$\Rightarrow d = \sqrt{5^{2} + {(- 4)}^{2} - 2 \cdot 5 \cdot (- 4) cos (\frac{7 π}{4} - π)}$ $implies d=sqrt(5^2+(-4)^2-2*5*(-4)Cos((7pi)/4-pi)$
$\Rightarrow d = \sqrt{25 + 16 + 40 cos (\frac{3 π}{4})}$ $implies d=sqrt(25+16+40Cos((3pi)/4)$
$\Rightarrow d = \sqrt{41 + 40 \cdot (- 0.7071)} = \sqrt{41 - 28.284} = \sqrt{12.716} = 3.56595$ $implies d=sqrt(41+40*(-0.7071))=sqrt(41-28.284)=sqrt(12.716)=3.56595$ units
$\Rightarrow d = 3.56595$ $implies d=3.56595$ units (approx)
Hence the distance between the given points is $3.56595$ $3.56595$ units.

Science

Math

Humanities

... and beyond

What is the distance between $(5, \frac{7 π}{4})$ $(5 , (7 pi)/4 )$ and $(- 4, π)$ $(-4 , pi )$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the distance between (5 , (7 pi)/4 )(5,7π4)(5 , (7 pi)/4 ) and (-4 , pi )(−4,π)(-4 , pi )?

1 Answer

Explanation:

Related questions

Impact of this question

What is the distance between $(5, \frac{7 π}{4})$ $(5 , (7 pi)/4 )$ and $(- 4, π)$ $(-4 , pi )$ ?