What is the distance between #(1 ,(3 pi)/4 )# and #(3 , (15 pi )/8 )#?

1 Answer
Shwetank Mauria
Mar 10, 2016

Distance between #(1,(3pi)/4)# and #(3,(15pi)/8)# is #3.9425#

Explanation:

#(r,theta)# in polar coordinates is #(rcostheta,rsintheta)# in rectangular coordinates.

Hence, #(1,(3pi)/4)# in rectangular coordinates is #(cos((3pi)/4),sin((3pi)/4))# or #(-sqrt2/2,sqrt2/2)# or #(-0.7071,0.7071)#

And #(3,(15pi)/8)# in rectangular coordinates is #(3cos((15pi)/8),3sin((15pi)/8))# or #(2.7716,-1.1481)#

Hence distance between #(-0.7071,0.7071)# and #(2.7716,-1.1481)# is

#sqrt((2.7716+0.7071)^2+(-1.1481-0.7071)^2)# or
#sqrt((3.4787)^2+(-1.8552)^2)# or
#sqrt(12.1014+3.4418)=sqrt(15.5432)=3.9425#

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