16. Parametric Equations & Polar Coordinates

Without calculating derivatives, determine the slopes of each of the lines tangent to the curve r=8 cos θ−4 at the origin.

49–52. Cartesian-to-polar coordinates Convert the following equations to polar coordinates.

(x - 1)² + y² = 1

49–52. Cartesian-to-polar coordinates Convert the following equations to polar coordinates.

y = 3

49–52. Cartesian-to-polar coordinates Convert the following equations to polar coordinates.

y = x²

37–48. Polar-to-Cartesian coordinates Convert the following equations to Cartesian coordinates. Describe the resulting curve.

r = 6 cos θ + 8 sin θ

37–48. Polar-to-Cartesian coordinates Convert the following equations to Cartesian coordinates. Describe the resulting curve.

r = 3 csc θ

37–48. Polar-to-Cartesian coordinates Convert the following equations to Cartesian coordinates. Describe the resulting curve.

r cos θ = -4

37–48. Polar-to-Cartesian coordinates Convert the following equations to Cartesian coordinates. Describe the resulting curve.

r = sin θ sec² θ

29–32. Intersection points Use algebraic methods to find as many intersection points of the following curves as possible. Use graphical methods to identify the remaining intersection points.

r = 2 cos θ and r = 1 + cos θ

29–32. Intersection points Use algebraic methods to find as many intersection points of the following curves as possible. Use graphical methods to identify the remaining intersection points.

r = 1 and r = 2 sin 2θ

31–36. Converting coordinates Express the following Cartesian coordinates in polar coordinates in at least two different ways.

(-4, 4√3)

31–36. Converting coordinates Express the following Cartesian coordinates in polar coordinates in at least two different ways.

(1, √3)

25–30. Converting coordinates Express the following polar coordinates in Cartesian coordinates.

(4, 5π)

25–30. Converting coordinates Express the following polar coordinates in Cartesian coordinates.

(2, 7π/4)

25–30. Converting coordinates Express the following polar coordinates in Cartesian coordinates.

(1, 2π/3)