Problems

In Problems 1-6, find tan ψ, where ψ is the angle between a line through the origin and the curve.

In Problems 7-25, sketch the given curve in polar coordinates by the method described in the text; 0 ≤ θ ≤ 2π unless stated otherwise.

In Problems 26-29, find the points where x and y have maxima and minima.

30            Find all points where the curves r = 1 + cos θ and r - 3 cos θ intersect.

31             Find all points where the curves r = ½ and r = sin(2θ) intersect. Warning: The points (r, θ) and ( - r,π + θ) are the same.

32            Find all points where the curves r = cosθ and r = sin (2θ) intersect.