The pectoral fins of a whale and a shark. Are they analogous organs?

The ancestors of all jawed animals probably had pectoral fins [Ref]. This primitive feature is homologous to shark pectoral fins (fig. 1). The forelimbs of quadrupeds are evolved from the pectoral fins of lobe-finned fish (fig. 2), and the pectoral fins of whales evolved from the forelimbs of their mammal ancestors. Thus, these organs are homologous as one can follow the gradual changes in morphology and find continuity between the fin to leg to fin transitions.

However, the internal structure of the fins themselves are quite different between whales and sharks as they evolved from a leg structure with fingers (fig. 3 & fig. 1). The external similarity of the fins is an example of convergent evolution, not directly the result of their shared origin. Some of the internal features of the fins may be homologous (I haven't checked), but you should not assume that a shared origin for the fins means they are the same.

Fig 1. Shark anatomy

Fig 2. Lobefinned fish and amphibian homologous limbs.

_{(source: ftexploring.com)}

Fig 3. Whale fin

Reference: 1. New study showing pelvic girdles arose before the origin of movable jaws, : Institute of Vertebrae Paleontology and Paleoanthropology, 2012

They are analogous at to function. Whales derive from terresterial animals that "returned" to the sea. Evolution adapted the forearms to fins. Here's a great diagram: http://evolution.berkeley.edu/evolibrary/article/evograms_03

The bat wing and the bird wing are also analogous as to function. Their functional aspects evolved independently. But as forelimbs they are homologous sharing a common ancestor with forelimbs.http://evolution.berkeley.edu/evolibrary/article/evo_09

We haven't yet answered the question of whether the whale fin and shark fin are homologous in origin: http://evolution.berkeley.edu/evolibrary/article/similarity_hs_09