What are polar coordinates?
How do you convert from polar to rectangular: x = ?
How do you convert from polar to rectangular: y = ?
How do you convert from rectangular to polar: r = ?
What polar equation produces a circle centered at the origin?
What shape does r = a + b·cos(θ) produce when a = b?
What shape does r = a·cos(nθ) produce?
What polar equation produces a vertical line x = a in rectangular coordinates?
Hint: Start from x = r·cos(θ) = a and solve for r
What shape does the polar equation r = a + b·cos(θ) produce when a < b?
Hint: Compare this to the cardioid case where a = b
What polar equation produces a line through the pole at angle θ = α?
Hint: The angle is fixed, but the distance from the pole can be anything
Convert the point (r, θ) = (4, π/2) to rectangular coordinates.
Hint: Use x = r·cos(θ) and y = r·sin(θ) with θ = π/2
Why can a single point in the plane have more than one polar coordinate representation?
Hint: Angles that differ by a full rotation land on the same ray