Thread: Cartesian and Polar Equations

1. Identify the curve: r*cos(theta) = 1 by finding a Cartesian equation for the curve.

2. Identify the curve: r = tan(theta)*sec(theta) by finding a Cartesian equation for the curve.

3. Find a polar equation for the curve represented by xy = 4.

Thanks for the help.

Originally Posted by eigenvector11

1. Identify the curve: r*cos(theta) = 1 by finding a Cartesian equation for the curve.

2. Identify the curve: r = tan(theta)*sec(theta) by finding a Cartesian equation for the curve.

3. Find a polar equation for the curve represented by xy = 4.

Thanks for the help.

by "Cartesian", I assume rectangular or (x,y).

x = r*cosT ------------cosT = x/r
y = r*sinT-----------------sinT = y/r
r = sqrt(x^2 +y^2)

1) r*cosT = 1
That is x = 1 -----------a vertical line, answer.

2) r = tanT*secT
r = sinT/cosT *1/cosT
r = sinT / cos^2(T)
r = (y/r) / (x/r)^2
r = ry / x^2
1 = y / x^2
x^2 = y
y = x^2 -------a vertical parabola that opens upward, answer.

3) xy = 4
(r*cosT)(r*sinT) = 4
(r^2)(sinTcosT) = 4
(r^2)((1/2)sin(2T)) = 4
(r^2)sin(2T) = 8
r^2 = 8/sin(2T)
r^2 = 8csc(2T)
r = 2sqrt[2csc(2T)] -----------answer.