What are the components of the vector between the origin and the polar coordinate $(6, \frac{3 π}{4})$ $(6, (3pi)/4)$ ?

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What are the components of the vector between the origin and the polar coordinate $(6, \frac{3 π}{4})$ $(6, (3pi)/4)$ ?

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Answer 1 · 2016-02-12T10:50:33

$((-3sqrt2),(3sqrt2))$

Explanation:

using the formulae that links Polar to Cartesian coordinates.

$• x = rcostheta$

$• y = rsintheta$

in this question: r = 6 and $theta = (3pi)/4$

$rArr x = 6cos((3pi)/4) = 6.(- 1/sqrt2) = -3sqrt2$

[note : $1/sqrt2 = sqrt2/(sqrt2 .sqrt2) = 1/2 sqrt2]$

and using exact values for $cos((3pi)/4)color(black)(" and ") sin((3pi)/4)$

$rArr y = 6sin((3pi)/4) = 6.(1/sqrt2) = 3sqrt2$

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What are the components of the vector between the origin and the polar coordinate $(6, \frac{3 π}{4})$ $(6, (3pi)/4)$ ?

1 Answer

Explanation:

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What are the components of the vector between the origin and the polar coordinate (6, (3pi)/4)(6,3π4)(6, (3pi)/4)?

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What are the components of the vector between the origin and the polar coordinate $(6, \frac{3 π}{4})$ $(6, (3pi)/4)$ ?