What is the distance between the following polar coordinates?: # (2,(3pi)/4), (1,(15pi)/8) #
3 Answers
Explanation:
We know that ,
We have ,
So ,
Explanation:
It is nontrivial to determine polar distances (since drawing a line in polar coordinates isn't very easy), so we should convert to Cartesian coordinates.
The first point is moderately easy:
The second point is a little harder, but we only need to use half angle identities. Let
Since
This allows us to use Pythagorean theorem in order to find the distance between the two points:
Pulling out a factor of
Using the cosine sum formula with
Therefore the total distance is
Explanation:
The distance between the points