Question #a0503

Question

What is the formula for converting polar coordinates to rectangular coordinates?
How do I convert polar coordinates $(5, 30^{\circ})$ $(5, 30^circ)$ to rectangular coordinates?
How do I convert polar coordinates $(3.6, 56.31)$ $(3.6, 56.31)$ to rectangular coordinates?
How do I convert polar coordinates $(10, - \frac{π}{4})$ $(10, -pi/4)$ to rectangular coordinates?
How do I convert polar coordinates $(4, - \frac{π}{3})$ $(4,-pi/3)$ to rectangular coordinates?
How do I convert polar coordinates $(6, 60^{\circ})$ $(6, 60^circ)$ to rectangular coordinates?
How do I convert polar coordinates $(- 4, 230^{\circ})$ $(-4, 230^circ)$ to rectangular coordinates?
What is the Cartesian equivalent of polar coordinates $(\sqrt{97}, 66^{\circ})$ $(sqrt97, 66^circ)$ ?
What is the Cartesian equivalent of polar coordinates $(2, \frac{π}{6})$ $(2, pi/6)$ ?
What is the Cartesian equivalent of polar coordinates $(7, π)$ $(7, pi)$ ?

1796 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-19T19:55:56

( $\sqrt{3}, 1$ $sqrt3, 1$ )

To make this change, we will use two equations:

$x = r cos (θ)$ $x=rcos(theta)$ and $y = r sin (θ)$ $y=rsin(theta)$

Our polar coordinate point is written in the form

$(r, θ)$ $(r, theta)$

So for the x coordinate we will plug in r and $θ$ $theta$ into the x equation

$x = (- 2) (cos (\frac{7 π}{6})) = (- 2) (- \frac{\sqrt{3}}{2}) = \sqrt{3}$ $x=(-2)(cos((7pi)/6)) = (-2)(-sqrt3/2) = sqrt3$

We will do the same for the y coordinate by plugging in the point values to the y equation

$y = (- 2) (sin (\frac{7 π}{6})) = (- 2) (- \frac{1}{2}) = 1$ $y=(-2)(sin((7pi)/6)) = (-2)(-1/2) = 1$

And we take those values and write them as a point

$(\sqrt{3}, 1)$ $(sqrt3, 1)$