Polar Coordinates

greatwhiteshark

Full Member
Joined
May 8, 2005
Messages
279
NOTE: t = theta, r = radius

Show that the formula for the distance d between two points
P1 = (r1, t1) = P2 = (r2, t2) is

d = sqrt{r1^2 + r2^2 - 2r1(r2)cos(t2 - t1)}
 
Since that's just the law of cosines I'm not sure what they want shown.
 
Gene

Gene,

The following data are all located in the radicand:

{r1^2 + r2^2 - 2r1(r2)cos(t2 - t1)}

Here's the question again:

NOTE: t = theta, r = radius

Show that the formula for the distance d between two points
P1 = (r1, t1) = P2 = (r2, t2) is

d = sqrt{r1^2 + r2^2 - 2r1(r2)cos(t2 - t1)}
 
polar1vz.gif
 
What I meant is if you call r1 "a" abd r2 "b" and t2-t1 "D" you have
d² = a²+b²-2abcos(D)
which is the law of cosines.
-----------------
Gene
 
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