(1) Let C be the polar curve defined by the equation r= 2(1sin).

(a) Graph C.

(b) Find the slope of its tangent when =/3.

(c) Find the points where C has horizontal tangents.

(d) Find the points where C has vertical tangents.

(e) Find the length of C.

(2) For each of the following statements, determine whether it is true or false. If it is true, prove it. If it is false, give a counter example to disprove it.

(a) If g(1) = 0 then the parametric curve defined by x=f(t) and y=g(t) has a horizontal tangent at t= 1.

(b) The length of a parametric curve defined by x=f(t) and y=g(t), where atb, is given by [a,b] [f(t)]^2+ [g(t)]^2dt.