What are the components of the vector between the origin and the polar coordinate $(- 7, \frac{- π}{4})$ $(-7, (-pi)/4)$ ?

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Answer 1 · 2017-11-14T09:34:57

$\frac{- 7 \sqrt{2}}{2} ˆ i + \frac{7 \sqrt{2}}{2} ˆ j$ $(-7sqrt(2))/2 hati +(7sqrt(2))/2 hatj$

This is much easier to solve if you convert the polar coordinates into Cartesian coordinates first. This can be achieved using:

$x = r cos θ$ $x=rcostheta$

$y = r sin θ$ $y=rsintheta$

$x = - 7 cos (\frac{- π}{4}) = \frac{- 7 \sqrt{2}}{2}$ $x=-7cos((-pi)/4)=(-7sqrt(2))/2$

$y = - 7 sin (\frac{- π}{4}) = \frac{7 \sqrt{2}}{2}$ $y=-7sin((-pi)/4)=(7sqrt(2))/2$

Cartesian coordinates:

$(\frac{- 7 \sqrt{2}}{2}, \frac{7 \sqrt{2}}{2})$ $((-7sqrt(2))/2 , (7sqrt(2))/2 )$