What are the components of the vector between the origin and the polar coordinate $(2, \frac{7 π}{4})$ $(2, (7pi)/4)$ ?

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What are the components of the vector between the origin and the polar coordinate $(2, \frac{7 π}{4})$ $(2, (7pi)/4)$ ?

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Answer 1 · 2016-02-16T07:07:25

Components of this vector from the origin are
{ $\sqrt{2}$ $sqrt 2$ , - $\sqrt{2}$ $sqrt 2$ j

Explanation:

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

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What are the components of the vector between the origin and the polar coordinate $(2, \frac{7 π}{4})$ $(2, (7pi)/4)$ ?

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Explanation:

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What are the components of the vector between the origin and the polar coordinate (2, (7pi)/4)(2,7π4)(2, (7pi)/4)?

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What are the components of the vector between the origin and the polar coordinate $(2, \frac{7 π}{4})$ $(2, (7pi)/4)$ ?