What are the components of the vector between the origin and the polar coordinate $(12, \frac{- 3 π}{8})$ $(12, (-3pi)/8)$ ?

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Answer 1 · 2018-04-10T11:58:02

$\to x = 4.59 ˆ i - 11.09 ˆ j$ $vec x = 4.59hat i - 11.09 hatj$

Polar coordinates of $\to x$ $vec x$ is

$(12, \frac{- 3 π}{8}); r = 12, θ = \frac{- 3 π}{8}$ $( 12,(-3pi)/8); r=12 , theta=(-3pi)/8$

$i$ $i$ component is $r cos θ or 12 \cdot cos (\frac{- 3 π}{8}) \approx 4.59$ $r cos theta or12*cos ((-3pi)/8)~~ 4.59$

$j$ $j$ component is $r sin θ or 12 \cdot sin (\frac{- 3 π}{8}) \approx - 11.09$ $r sin theta or 12*sin ((-3pi)/8)~~ -11.09$

$:.vec x = 4.59 hati - 11.09 hat j$ [Ans]

What are the components of the vector between the origin and the polar coordinate (12, (-3pi)/8)(12,−3π8)(12, (-3pi)/8)?