What is the distance between #(1 ,( pi)/4 )# and #(-1 , ( 3 pi )/2 )#? Trigonometry The Polar System Polar Coordinates 1 Answer ali ergin Mar 27, 2016 #s=0,77" unit"# Explanation: #"use the formula :" s=sqrt(r_1^2+r_2^2-2*r_1*r_2*cos(theta_2-theta_1))# #"the form of the polar coordinate:"# #P_1=(r_1,theta_1)# #P_2=(r_2,theta_2)# #P_1=(1,pi/4)# #P_2=(-1,(3pi)/2)# #theta_2-theta_1=(3pi)/2-pi/4)=(5pi)/4# #s=sqrt(1^2+(-1)^2+2*1*1*cos (5pi)/4)# #s=sqrt(1+1+2*(-0,707)# #s=sqrt(2-1,414)# #s=sqrt(0,586)# #s=0,77# 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 1493 views around the world You can reuse this answer Creative Commons License