How do you convert the Cartesian coordinates (0,-10) to polar coordinates?

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Answer 1 · 2015-09-12T22:12:07

#(r,theta)=(10,(3pi)/2)#

When converting from Cartesian to polar coordinates we use the following relationships

#x=rcostheta#

#y=rsintheta#

#r=sqrt(x^2+y^2)#

We are given the point #(0,-10)#

Proceed by finding #r#. Since #r# is a length we only want the positive square root.

#r=sqrt((0)^2+(-10)^2)#

#r=sqrt100=10#

Now we utilize the other relationships

#x=rcostheta# so we can write

#0=10costheta#

So #costheta=0#

We know that we are on the y axis at #x=0# and #y=-10# so our angle is

#theta=(3pi)/2#

Also

#y=rsintheta# so we can write

#-10=10sintheta#

#sintheta=-1#

This occurs when #theta=(3pi)/2#

Therefore #(r,theta)=(10,(3pi)/2)#

Make sure your calculator is in radians