How do I convert polar coordinates $(- 4, 230^{\circ})$ $(-4, 230^circ)$ to rectangular coordinates?

Question

3061 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-09-30T04:06:37

$(r, θ) \to (- 4, 230)$ $(r,theta)->(-4,230)$

$230^{\circ}$ $230^circ$ has to be converted to radians.

Degrees to Radians

$230^{\circ} \cdot \frac{π}{180^{\circ}} = \frac{230 π}{180} = \frac{23 π}{18}$ $230^circ*pi/180^circ=(230pi)/180=(23pi)/18$

Polar to Rectangular

$x = r cos (θ) = (- 4) \cdot cos (\frac{23 π}{18}) = - 4 (- 0.6428) = 2.5712$ $x=rcos(theta)=(-4)*cos((23pi)/18)=-4(-0.6428)=2.5712$

$y = r sin (θ) = (- 4) \cdot sin (\frac{23 π}{18}) = - 4 (- 0.7660) = 3.0641$ $y=rsin(theta)=(-4)*sin((23pi)/18)=-4(-0.7660)=3.0641$

$(r, θ) \to (- 4, 230)$ $(r,theta)->(-4, 230)$
$(x, y) \to (2.5712, 3.0641)$ $(x,y)->(2.5712, 3.0641)$

How do I convert polar coordinates (−4,230∘)(-4, 230^circ) to rectangular coordinates?