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

Answer 1

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)#.

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.