Given the polar curve r = 2sin(3theta) --------- (I) [1] With the aid of a graphing calculator, sketch the region enclosed by polar curve (I). Specify the minimal range of theta required, label the orientation of the curve. [2] Find the equation of the tangent line(s) at the pole if any. Justify your answers. ? write the equation in polar coordinates [3] Find the point(s) of r = 2sin(3theta) where the tangent line is horizontal. Show work to justify your answer(s).

Given the polar curve r = 2sin(3theta) --------- (I)
[1] With the aid of a graphing calculator, sketch the region enclosed by polar curve (I).

Specify the minimal range of theta required, label the orientation of the curve. [2] Find the equation of the tangent line(s) at the pole if any. Justify your answers.

? write the equation in polar coordinates
[3] Find the point(s) of r = 2sin(3theta) where the tangent line is horizontal. Show work to justify your answer(s).

[4] Write the integral for the area of that pedal of r = 2sin(3theta) in the 2nd Quadrant.
[5] Find the area of one pedal of r = 2sin(3theta) in the first quadrant

Show all work to justify your answer. Write your answer in exact form.
[6] With the aid of a calculator, estimate the arc length of one pedal of r = 2sin(3theta) in the first quadrant. Round your answer to 4-decimal places.