What is the distance between $(2, \frac{3 π}{4})$ $(2 ,(3 pi)/4 )$ and $(2, \frac{11 π}{8})$ $(2 , (11 pi )/8 )$ ?

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Answer 1 · 2016-10-21T09:28:51

The distance between given points is $3.326$ $3.326$ .

The distance between two points given their polar coordinates $(r_{1}, θ_{1})$ $(r_1,theta_1)$ and $(r_{2}, θ_{2})$ $(r_2,theta_2)$ is given by

$\sqrt{r_{1}^{2} + r_{2}^{2} - 2 r_{1} r_{2} cos (θ_{1} - θ_{2})}$ $sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2))$

Hence, distance between $(2, \frac{3 π}{4})$ $(2,(3pi)/4)$ and $(2, \frac{11 π}{8})$ $(2,(11pi)/8)$ is

$\sqrt{2^{2} + 2^{2} - 2 \times 2 \times 2 \times cos (\frac{11 π}{8} - \frac{3 π}{4})}$ $sqrt(2^2+2^2-2xx2xx2xxcos((11pi)/8-(3pi)/4))$

= $\sqrt{4 + 4 - 8 cos (\frac{5 π}{8})}$ $sqrt(4+4-8cos((5pi)/8)$

= $\sqrt{8 \times (1 - (- 0.3827))}$ $sqrt(8xx(1-(-0.3827))$

= $\sqrt{8 \times 1.3827}$ $sqrt(8xx1.3827)$

= $\sqrt{11.0616}$ $sqrt11.0616$

= $3.326$ $3.326$
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What is the distance between (2,3π4)(2 ,(3 pi)/4 ) and (2,11π8)(2 , (11 pi )/8 )?