Field at a point on the axis of a ring with variable charge density

[JesseAbberton]

Homework Statement

is the given charge density, is constant and Is the azimuthal angle. R is the radius and we have to find field at a point r distance from the centre of ring as a function of r.

I have great confusion regarding the question after reading the solution from the book. They haven't really correctly done the sign of the charge density if they have taken the angle as follows and the diagram i found a bit vague. Could somebody please help me out here? Thank you :)

 

[kuruman]

You need to be more more specific about what you don't understand otherwise we cannot help you.

What is vague about the diagram? It shows how the electric field vector element $d\mathbf E$ is resolved along the three Cartesian axes $x$, $y$ and $z$.
What charge density have they not done correctly? If you know what the correct form for the charge density is, please post it and explain why you think it is what you say.
Also, it is much easier for us to help you if you post your equations in LaTeX. To learn how to do that, click on the link "LaTeX Guide", lower left above "Attach Files."