How do you find the rectangular coordinates of the point with polar coordinates $(5, \frac{π}{2})$ $(5,pi/2)$ ?

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How do you find the rectangular coordinates of the point with polar coordinates $(5, \frac{π}{2})$ $(5,pi/2)$ ?

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Answer 1 · 2014-08-24T20:00:57

To convert from from polar coordinates to rectangular coordinates, we must remember these:

$x = r cos θ$ $x = rcostheta$
$y = r sin θ$ $y = rsintheta$

It's useful to remember these when we need to do these types of conversions. Knowing the $r$ $r$ and $θ$ $theta$ from our question, we can find the rectangular coordinates:

$r = 5$ $r=5$

$θ = \frac{π}{2}$ $theta=pi/2$

$x = (5) cos (\frac{π}{2}) = (5) (0) = 0$ $x=(5)cos(pi/2) = (5)(0) = 0$
$y = (5) sin (\frac{π}{2}) = (5) (1) = 5$ $y=(5)sin(pi/2) = (5)(1) = 5$

Therefore, our rectangular coordinates are:

$(0, 5)$ $(0,5)$

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How do you find the rectangular coordinates of the point with polar coordinates $(5, \frac{π}{2})$ $(5,pi/2)$ ?

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