What are the components of the vector between the origin and the polar coordinate $(- 5, \frac{- 3 π}{4})$ $(-5, (-3pi)/4)$ ?

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What are the components of the vector between the origin and the polar coordinate $(- 5, \frac{- 3 π}{4})$ $(-5, (-3pi)/4)$ ?

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Answer 1 · 2018-02-27T06:00:41

Rectangular coordinates are $(3.5355, 3.5355)$ $color(indigo)((3.5355, 3.5355)$ or $(\frac{5}{\sqrt{2}}, \frac{5}{\sqrt{2}})$ $color(indigo)((5/sqrt2, 5/sqrt2)$

Explanation:

Given $r = - 5, θ = - \frac{3 π}{4}$ $r = -5, theta = -(3pi)/4$

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To find the Cartesian coordinates.

$x = r cos θ = - 5 \cdot cos (\frac{- 3 π}{4}) = 3.5355$ $x = r cos theta = -5 * cos ((-3pi)/4) = color(indigo)(3.5355)$

$y = r sin θ = - 5 \cdot sin (\frac{- 3 π}{4}) = 3.5355$ $y = r sin theta = -5 * sin ((-3pi)/4) = color(indigo)(3.5355)$

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What are the components of the vector between the origin and the polar coordinate $(- 5, \frac{- 3 π}{4})$ $(-5, (-3pi)/4)$ ?

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Explanation:

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What are the components of the vector between the origin and the polar coordinate $(- 5, \frac{- 3 π}{4})$ $(-5, (-3pi)/4)$ ?