2.5.8 Plotting functions

Condition: Given a function \( r=f(\varphi) \) on the interval \( 0 \leq \varphi \leq 2 \pi \). 1) Construct a graph of the function in the polar coordinate system by points, giving \( \varphi \) values ​​through the interval \( \pi / 8 \), starting from \( \varphi=0 \); 2) Find the equation of the resulting line in a rectangular Cartesian coordinate system, the origin of which coincides with the pole, and the positive semi-abscissa axis coincides with the polar axis, and from the equation determine what kind of line it will be. \[ r=\frac{-2}{\cos \varphi} \]