1. The problem statement, all variables and given/known data Hello! I am struggling with plotting polar graphs manually (without any help of the calculator). My main unresolved issue is with finding correct values of theta in a given range. For example, I have an equation: $r = cos(5\theta)$ 2. Relevant equations and I know that the range I have to work with is [-π/5 , π/5]. Here are the values I get when arbitrary choose values of theta to compute r, then x and y. But the problem is that I don't know of any algorithm that I could apply in any such case to choose correct values of theta - here I started with -π/5, took π/6, next π/10, and 0 for the first half. I suppose there should be some algorithm or rules applicable for such choices. Please, help me to fill that gap in my knowledge. 3. The attempt at a solution Thank you very much!