3. Sketch the curve with the given polar equation. (a) r = 2 sin 0 (b) r = 3(1 cos 0) (c) r=sin(30) (three-leaved rose.)

6. (i) Convert the equation (x – 2)2 + y? = 4 from cartesian to polar (ii) Convert the equation r2 = 4r sin 0 from polar to cartesian.

Find the slope of the tangent line to the polar curve r = 2sinθ +1 atθ= π/4 and then find its equation.

3. (b) Identify the curve by transforming the given polar equation to rectangular equations. r= 6 3 cos 0+2 sin

PLEASE PLEASE PLEASE HELP, I have one last try left.  By the relation between the polar and Cartesian coordinate systems, x = r cos(?).  Substituting for r from the equation of the given curve,  x = ( ??? )cos(?) = sin2(?).