How do you find the distance between the points with the given polar coordinates #P_1(4,170^circ)# and #P_2(6,105^circ)#?

1 Answer
Bdub
Nov 30, 2016

#d~~5.63#

Explanation:

Each point on a polar plane is represented by the ordered pair #(r,theta)#.

So lets call the coordinates of #P_1# as #(r_1,theta_1)# and coordinates of #P_2# as #(r_2,theta_2)# . To find the distance between two points on a polar plane use the formula #d=sqrt((r_1) ^2+(r_2)^2-2r_1r_2cos(theta_2-theta_1))#

Thererfore using the points #(4,170^@)# and #(6,105^@)#, and the formula

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

we have

#d=sqrt(4 ^2+6^2-2*4*6cos(105-170))#

#:. d~~5.63#

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