What are the components of the vector between the origin and the polar coordinate $(2, \frac{5 π}{4})$ $(2, (5pi)/4)$ ?

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Answer 1 · 2017-12-10T12:09:12

$- \sqrt{2} ˆ i - \sqrt{2} ˆ j$ $-sqrt(2)hati-sqrt(2)hatj$

First convert the polar coordinates to Cartesian coordinates. This can be done using the following idea:

Cartesian coordinate is equal to:

$(r cos θ, r sin θ)$ $(rcostheta , rsintheta)$

$:.$

$x=rcostheta$

$y=rsintheta$

$x=2cos((5pi)/4)=-sqrt(2)$

$y=2sin((5pi)/4)=-sqrt(2)$

The component vector for $x$ is $hati$

and the component vector for $y$ is $hatj$

$:.$

$-sqrt(2)hati-sqrt(2)hatj$

What are the components of the vector between the origin and the polar coordinate (2, (5pi)/4)(2,5π4)(2, (5pi)/4)?