What is the distance between the following polar coordinates?: # (1,(-5pi)/12), (3,(pi)/8) #

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Answer 1 · 2017-04-15T19:55:05

#3.284#

Write each polar point as a cartesian point using parametric equations.

#x=rcos(theta)#

#y=rsin(theta)#

For #(1,-5pi/12)#

#x(t) = 1 cos(-5pi/12) ~~ .259#

#y(t)= 1 sin(-5pi/12) ~~ -.966#

For #(3,pi/8)#

#x= 3 cos(pi/8) ~~ 2.772#

#y=3 sin(pi/8) ~~ 1.148#

So now we have the points in cartesian form:

#(.259,-.966), (2.772,1.148)#

Use distance formula:

#d=sqrt((2.772-.259)^2+(1.148-(-.966))^2)~~3.284#