Step 1

To express the given curve in cartesian coordinates (x and y), using the transformation equations from the polar to the cartesian

Step 2

Transformation equations:

\(x=r\cos 0, y=r\sin 0, r^{2}=x^{2}+y^{2}\)...(1)

Given

\(r=5\sin 0\)...(2)

Step 3

Mutiply (2) by r and use the relation \(r^{2}=x^{2}+y^{2}\) to obtain the required Cartesian equation

\(r\times (2):r^{2}=5r\sin 0\)

Apply (1) to get

\(x^{2}+y^{2}=5y\), or

\(x^{2}+y^{2}-5y=0\)

Step 4

Answer: \(x^{2}+y^{2}-5y=0\)

To express the given curve in cartesian coordinates (x and y), using the transformation equations from the polar to the cartesian

Step 2

Transformation equations:

\(x=r\cos 0, y=r\sin 0, r^{2}=x^{2}+y^{2}\)...(1)

Given

\(r=5\sin 0\)...(2)

Step 3

Mutiply (2) by r and use the relation \(r^{2}=x^{2}+y^{2}\) to obtain the required Cartesian equation

\(r\times (2):r^{2}=5r\sin 0\)

Apply (1) to get

\(x^{2}+y^{2}=5y\), or

\(x^{2}+y^{2}-5y=0\)

Step 4

Answer: \(x^{2}+y^{2}-5y=0\)