Math 266 page 714 #27 (11.3) (5th edition)
For each of the described curves, decide if the curve would be more easily given by a
polar equation or a Cartesian equation. Then write an equation for the curve.
#27. (a) A line through the origin that makes an angle of

with the positive x  axis.
6
Solution:
maple program
> plot([t,Pi/6,t=0..6],coords=polar,scaling=CONSTRAINED);

:polar equation.
6
 
(ii) slope  tan   .
6
1
Thus y  x :Cartesian equation.
2
(b) vertical line through the point (3,3) .
Solution:
maple program
> > plot([3*sec(t),t,t=-0.9..0.9],x=-1..4,y=1..4,coords=polar);
(i)  
>
(i) r cos  3 : polar equation
(ii) x  3 :Cartesian equation.