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

1 Answer
Sep 12, 2015

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

Explanation:

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