Question

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

Answer 1

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)