What is the distance between the following polar coordinates?: (1,(-5pi)/12), (5,(11pi)/8)

1 Answer
sankarankalyanam
Oct 15, 2017

Distance = 5.0206

Explanation:

Distance between two points with polar coordinates :
d = sqrt(r1^2 + r2^2- 2r1r2(cos (theta1 -theta2)))
Given
r_1 = 1, r_2 = 5, theta_1 = -((5pi)/2), theta_2 = (11pi)/2
d = sqrt(1 + 25 - (2*1*5*(cos ((-5pi)/12)-((11pi)/8))
= sqrt(26- 10 cos(-(43pi)/24)
= sqrt (26-10cos((43pi)/24)) = sqrt(26 - 10*0.7934
d = sqrt(25.2066) = 5.0206

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