Question

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

Answer 1

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`