What is the distance between the following polar coordinates?: # (3,(7pi)/12), (1,(17pi)/8) #

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Answer 1 · 2017-06-07T10:50:06

#D~~3.04#

The distance formula for rectangular coordinates is

#D=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

Plugging in #x_n=r_ncos(theta_n)# and #y_n=r_nsin(theta_n)#, expanding, and simplifying gives

#D=sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2))#

Plugging in #(r_1,theta_1)=(3,(7pi)/12)# and #(r_2,theta_2)=(1,(17pi)/8)#

#D=sqrt(3^2+1^1-2(3)(1)cos((17pi)/8-(7pi)/12))#

#D=sqrt(10-6cos((37pi)/24))#

#D~~3.04#