16. Parametric Equations & Polar Coordinates

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)

Plot the points with polar coordinates (2, π/6) and (−3, −π/2). Give two alternative sets of coordinate pairs for both points.

Write the equations that are used to express a point with polar coordinates (r, θ) in Cartesian coordinates.

What is the polar equation of the horizontal line y = 5?

Given three polar coordinate representations for the origin.

9–13. Graph the points with the following polar coordinates. Give two alternative representations of the points in polar coordinates.

(-1, -π/3)

9–13. Graph the points with the following polar coordinates. Give two alternative representations of the points in polar coordinates.

(-4, 3π/2)