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

Question

6787 views around the world

You can reuse this answer
Creative Commons License

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)#