Question

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

Answer 1

Distance: `color(green)(sqrt(122)`

Explanation:

Note that these points (relative to the origin) are at right angles to each other (since `(5pi)/8-pi/8=pi/2`).

Therefore we are looking at a right triangle with arms of length `1` and `11`
and a distance between them equal to the hypotenuse.

Using the Pythagorean Theorem, this distance is
`color(white)("XXX")sqrt(1^2+11^2)=sqrt(122)`