  The cosine-$\lambda$ transform, denoted $\mathcal{C}^\lambda$, is a family of
integral transforms we can define on the sphere and on the Grassmann manifolds
$\textrm{Gr}(p, \mathbb{K}^n) =
\textrm{SU}(n,\mathbb{K})/\text{S}(\textrm{U}(p,\mathbb{K}) \times
\textrm{U}(n-p,\mathbb{K}))$ where $\mathbb{K}$ is $\mathbb{R}$, $\mathbb{C}$
or the skew field $\mathbb{H}$ of quaternions. The family $\mathcal{C}^\lambda$
extends meromorphically in $\lambda$ to the complex plane with poles at (among
other values) $\lambda =-1,\ldots, -p$. In this paper we normalize
$\mathcal{C}^\lambda$ and evaluate at those poles. The result is a series of
integral transforms on the Grassmannians that we can view as partial
cosine-Funk transforms. The transform that arises at $\lambda = -p$ is the
natural analog of the Funk transform in this setting.
