Why Kenneth Krane uses $ \mathbf {k} \cdot \mathbf {r} = kr \sin\theta$? While discussing the topic "The Distribution of Nuclear Charge" in "Introductory Nuclear Physics" Kenneth Krane substitutes $ \ $ $\mathbf {k} \cdot \mathbf {r} = kr \sin\theta$ $ \ $ in equation 3.2 to get equation 3.5
But conventionally the Dot Product of TWO vectors $\mathbf{A}$ and $\mathbf{B}$ is defined as $\mathbf {A} \cdot \mathbf {B} = AB\cos\theta$
Why this particular substitution is used instead of $\mathbf {k} \cdot \mathbf {r} = kr  \cos\theta$ ? 
Please refer to the the Pages from the Book:-



 A: It's because equations 3.1 - 3.6 are working in spherical coordinates, with r as the radial coordinate, $\theta$ the polar coordinate, and $\phi$ the azimuthal coordinate, and because Krane is picking a convenient coordinate frame. An expression for the dot product of two vectors in spherical coordinates, based on this answer is:
$\textbf{q $\cdot$ r}$ 
= ($|\textbf{q}|,\theta_q, \phi_q$) $\cdot$ ($|\textbf{r}|,\theta_r$, $\phi_r$) 
= $qr$[sin($\theta_q$)sin($\theta_r$)cos($\phi_q$ - $\phi_r$) + cos($\theta_q$)cos($\theta_r$)]
Since the integration in equation 3.2 is over all space, we can take some liberties with the coordinate system orientation. Pick a system so that the $\textbf{q}$ and $\textbf{r}$ are in a plane defined by $\phi_q, \phi_r = 0$. Additionally, orient the coordinate system so that the polar axis is orthogonal to $\theta_r$, i.e such that $\theta_r = {\pi}/2$. In this frame the expression for the dot product reduces to:
$\textbf{q$\cdot$r} = qr$ sin($\theta_q$)
At this point the subscript can be dropped.
