WARNING: This Study Guide does NOT use the same conventions for spherical coordinates as those used in your text. Instead, the Study Guide uses the most commonly used choice in science and engineering applications, explicitly given by $$x=r\sin\theta\cos\phi \qquad y=r\sin\theta\sin\phi \qquad z=r\cos\theta$$ You will often see $\rho$ (or $R$) instead of $r$, and/or the roles of $\theta$ and $\phi$ interchanged. However, spherical coordinates should ALWAYS be given in the following order: $$\hbox{(radius, angle from $z$-axis, angle in $xy$-plane)}$$ For us this is $(r,\theta,\phi)$. BE CAREFUL to correctly translate the text's notation! You should feel free to use whichever convention you are most comfortable with, but you should be aware that other conventions exist, and that your text's choice is not widely used outside the mathematics community. 1)

We will also adopt the convention used in some science and engineering texts and use $\phi$ rather than $\theta$ for polar coordinates, so that the angle in the $xy$-plane is always $\phi$. We therefore write $$x=r\cos\phi \qquad y=r\sin\phi$$ Again, this is not the choice used by your textbook; be careful!