Question

What is the distance between the following polar coordinates?: `(4,(-11pi)/12), (1,(-7pi)/8)`

Answer 1

`P_1P_2=sqrt(9.068441109) ~~3.01`

Explanation:

Distance formula in Polar form:`P_1P_2=sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_2-theta_1))`
`r_1=4, theta_1=(-11pi)/12, r_2=1,theta_2=(-7pi)/8`

`P_1P_2=sqrt(4^2+1^2-2(4)(1)cos((-7pi)/8-(-11pi)/12))`

`P_1P_2=sqrt(16+1-8cos((pi)/24))`

`P_1P_2=sqrt(17-8cos((pi)/24))`

`P_1P_2=sqrt(9.068441109) ~~3.01`