What is the distance between the following polar coordinates?: (3,(-7pi)/12), (7,(5pi)/8)

1 Answer
Jan 6, 2016

9.556 units.

Explanation:

The distance formula for polar coordinates is

d=sqrt(r_1^2+r_2^2-2r_1r_2Cos(theta_1-theta_2)
Where d is the distance between the two points, r_1, and theta_1 are the polar coordinates of one point and r_2 and theta_2 are the polar coordinates of another point.
Let (r_1,theta_1) represent (3,(-7pi)/12) and (r_2,theta_2) represent (7,(5pi)/8).
implies d=sqrt(3^2+7^2-2*3*7Cos((-7pi)/12-(5pi)/8)
implies d=sqrt(9+49-42Cos((-14pi-15pi)/24)
implies d=sqrt(58-42Cos((-29pi)/24))=sqrt(58-42*(-0.7933))=sqrt(58+33.3186)=sqrt(91.3186)=9.556 units
implies d=9.556 units (approx)
Hence the distance between the given points is 9.556 units.