What are the components of the vector between the origin and the polar coordinate #(2, (7pi)/4)#?

1 Answer
A. S. Adikesavan
Feb 16, 2016

Components of this vector from the origin are
{#sqrt 2#, - #sqrt 2#j

Explanation:

r = 2 and #theta# = #7pi#/4.
The radial line #theta# = 7#pi#/4 bisects the fourth quadrant..
x = 2 cos #7pi#/4 =2 cos (#2pi - pi#/4) = 2 cos (#pi#/4) = #sqrt# 2. Similarly, y = 2 sin #7pi#/4 =2sin (#2pi - pi#/4) = - 2 sin (#pi#/4) = - #sqrt#2.
The given radial vector has components (x, y) = (#sqrt#2, - #sqrt#2)

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