What are the components of the vector between the origin and the polar coordinate $(5, π)$ $(5, pi)$ ?

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What are the components of the vector between the origin and the polar coordinate $(5, π)$ $(5, pi)$ ?

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Answer 1 · 2018-03-21T15:46:36

$(x, y) \equiv (- 5, 0)$ $(x,y)-=(-5,0)$

Explanation:

Given:
$r = 5$ $r=5$
$θ = π$ $theta=pi$

$x = r cos θ$ $x=rcostheta$
$\Rightarrow r cos θ = 5 cos π$ $=>rcostheta=5cospi$
$\Rightarrow cos π = - 1$ $=>cospi=-1$
$\Rightarrow 5 cos π = 5 \times - 1$ $=>5cospi=5xx-1$
$\Rightarrow r cos θ = - 5$ $=>rcostheta=color(blue)(-5)$

$y = r sin θ$ $y=rsintheta$
$\Rightarrow r sin θ = 5 sin π$ $=>rsintheta=5sinpi$
$\Rightarrow sin π = 0$ $=>sinpi=0$
$\Rightarrow 5 sin π = 5 \times 0$ $=>5sinpi=5xx0$
$\Rightarrow r sin θ = 0$ $=>rsintheta=color(blue)(0)$

$(x, y) \equiv (- 5, 0)$ $(x,y)-=(-5,0)$

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What are the components of the vector between the origin and the polar coordinate $(5, π)$ $(5, pi)$ ?

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Explanation:

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