How do you find the rectangular coordinates of the point with polar coordinates $(-1,pi/3)$ ?

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Answer 1 · 2014-09-27T02:18:42

When trying to convert polar coords to rectangular coords or vice versa you need to be aware of a few equations.

$cos(theta)=x/r -> x=rcos(theta)$

$sin(theta)=y/r -> y=rsin(theta)$

$tan(theta)=y/x -> theta = tan^-1(y/x)$

$x^2+y^2=r^2 -> r=sqrt(x^2+y^2)$

Polar Coordinates

$(r,theta) -> (-1,pi/3)$

Calculate the $x$ -value

$x=rcos(theta)$

$x=(-1)*cos(pi/3)$

$x=(-1)(1/2)$

$x=-1/2$

Calculate the $y$ -value

$y=rsin(theta)$

$y=(-1)(sqrt(3)/2)$

$y=-sqrt(3)/2$

Rectangular Coordinates

$(x,y)->(-1/2,-sqrt(3)/2)$

How do you find the rectangular coordinates of the point with polar coordinates (-1,pi/3)(-1,pi/3)?