What are the components of the vector between the origin and the polar coordinate #(25, (-pi)/6)#?

1 Answer
David G.
Jan 31, 2016

In practice, this question simply asks for the coordinates to be converted from polar to rectangular (Cartesian) coordinates, since the components of the vector will be the #x# and #y# distances. In this case, #(21.7, -12.5)#.

Explanation:

The components of the vector are simply the #x# and #y# coordinates of the point at its tip. We are given the polar coordinates of that point but need the rectangular coordinates:

#x=rcostheta = 25 cos (-pi/6) = 25*0.866 = 21.7#

#t=rsintheta = 25 sin (-pi/6) = 25*(-0.5) = -12.5#

That means the coordinates of the point at the tip of the vector are #(21.7, -12.5)#.

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