Question

What is the distance between the following polar coordinates?: `(2,(pi)/4), (3,(13pi)/8)`

Answer 1

`d = 4.90781`

Explanation:

First we pass the points in polar coordinates to Cartesian. The pass equations are
`x = r cos(theta)`
`y = r sin(theta)`
`(2,pi/2)->(2 cos(pi/2),2 sin(pi/2))=(0,2) = (x_1,y_1)`
`(3,(13pi)/8)->(3 cos((13pi)/8),3 sin((13pi)/8)) =(1.14805, -2.77164) = (x_2,y_2)`
Now we calculate the distance `d = sqrt((x_1-x_2)^2+(y_1-y_2)²) = 4.90781`