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

1 Answer
Sep 12, 2015

(r,θ)=(10,3π2)

Explanation:

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

x=rcosθ

y=rsinθ

r=x2+y2

We are given the point (0,10)

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

r=(0)2+(10)2

r=100=10

Now we utilize the other relationships

x=rcosθ so we can write

0=10cosθ

So cosθ=0

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

θ=3π2

Also

y=rsinθ so we can write

10=10sinθ

sinθ=1

This occurs when θ=3π2

Therefore (r,θ)=(10,3π2)

Make sure your calculator is in radians