How do you convert the rectangular point #(-sqrt3,1)# into polar form?

Question

7580 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-16T11:33:24

The polar coordinates are #(2,(5pi)/6)#

To convert rectangular coordinates to polar coordinates, we use the following equations

#x=rcostheta#

#y=rsintheta#

#x^2+y^2=r^2#

#(x,y)=(-sqrt3,1)#
Therefore, #r^2=(-sqrt3)^2+1=4#

So, #r=2#

#-sqrt3=2costheta# and #1=2sintheta#

#costheta=-sqrt3/2#

and #sintheta=1/2#

#theta# is in the second quadrant, and ##theta=5pi/6

So, the polar coordinates are #(2,(5pi)/6)#