For the Nikon F mount, the cited geometric argument is plausible: if the maximum angular aperture is about 54°, the corresponding minimum f-number is approximately 1/(2·sin(54°/2)) ≈ f/1.1. That logic is sound for a mount-geometry analysis, and using sine rather than tangent is the correct approach in that context.

That said, this is best understood as a practical/geometric limit for conventional optical designs using that mount, not proof of an absolute universal limit on lens aperture. In real lens design, many “soft limits” matter: rear element size, flange distance, optical complexity, physical size, weight, cost, and correction of aberrations. As apertures get larger, lenses become disproportionately bigger and more difficult to design and manufacture.

So the short answer is: yes, the schematic’s reasoning appears credible for estimating a Nikon F-mount practical minimum f-number around f/1.1, but lens design is governed by both mount geometry and significant real-world engineering constraints.