What is the distance between #(4 ,( 9 pi)/8 )# and #(-4 ,( 3pi )/2 )#?

1 Answer
Harish Chandra Rajpoot
Jul 19, 2018

#6.6517\ \text{unit}#

Explanation:

The distance between the points #(r_1, \theta_1)\equiv(4, {9\pi}/8)# & #(r_2, \theta_2)\equiv(-4, {3\pi}/2)# is given by the formula as follows

#\sqrt{r_1^2+r_2^2-2r_1r_2\cos(\theta_1-\theta_2)}#

#=\sqrt{4^2+(-4)^2-2(4)(-4)\cos({9\pi}/8-{3\pi}/2)}#

#=\sqrt{32+32\cos({3\pi}/8)}#

#=4\sqrt2\sqrt{1+\sin({\pi}/8)}#

#=6.6517\ \text{unit}#

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