Question

What is the distance between the following polar coordinates?: `(4,(7pi)/4), (3,(3pi)/8)`

Answer 1

`5.8508` 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 `(4,(7pi)/4)` and `(r_2,theta_2)` represent `(3,(3pi)/8)`.
`implies d=sqrt(4^2+3^2-2*4*3Cos((7pi)/4-(3pi)/8)`
`implies d=sqrt(16+9-24Cos((11pi)/8)`
`implies d=sqrt(25-24*(-0.3847))=sqrt(25+9.2328)=sqrt(34.2328)=5.8508` units
`implies d=5.8508` units (approx)
Hence the distance between the given points is `5.8508`.