What is the distance between #(4 ,( 9 pi)/8 )# and #(-4 ,( 3pi )/2 )#? Trigonometry The Polar System Polar Coordinates 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}# Answer link Related questions What are Polar Coordinates? How do you find the polar coordinates of the point? What is the difference between a rectangular coordinate system and a polar coordinate system? How do you graph polar coordinates? What careers use polar coordinates? How do you plot the point #A (5, -255^\circ)# and the point #B (3, 60^\circ)#? What does a polar coordinate system look like? How do you find the distance between 2 polar coordinates? For the given point #A(-4, frac{pi}{4})#, how do you list three different pairs of polar... How do you find the rectangular form of #(4, -pi/2)#? See all questions in Polar Coordinates Impact of this question 1508 views around the world You can reuse this answer Creative Commons License