3. Sketching in polar coordinates

a) Sketch the curve defined by the equation r =

cos(20)

b) Sketch the region that lies inside the circle

r = 3 sin(0) and outside the cardioid r = 1+ sin/nc) Sketch the region: R= {(r, 0) : -/4 ≤ 0 ≤d) Sketch the region: R = {(r, 0) T ≤ 0 ≤

π/4,1 < r ≤ 2} and find its area.

3π/2,1 ≤ r ≤ 2} and find its area./ne) Sketch by hand the region:

R = {(x,y) : x ≤ y ≤ √√2-x²,0 ≤ x ≤ 1}.

f) Find the volume under the surface defined by

f(x, y) = y(x² + y²) ²

over the region R (see left) in the plane z = 0.

Convert this integral to polar coordinates and

evaluate it.