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For sensors much smaller than the focal length (as in your case), you can ignore any trigonometric functions and simply get the approximate FOV in degrees using

I am running the camera at 720P, a 16:9 aspect ratio. I am not sure if the sensor is 4:3 or 16:9, physically... Googling seems to suggest all sensors are 4:3 but this camera doesn't support any 4:3 resolutions so I don't know.

If I use this lens with this camera, given that the sensor size differs from the specs of the lens and that I'm running at 16:9, how can I calculate the effective horizontal and vertical FOV of the image?

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I don't really understand the meaning of a lot of these numbers but I'm assuming that 1/2.8" is the diagonal, which means the sensor dimensions are something like 7.9mm x 4.45mm.

You see, for FOV calculation, you just need the lens focal length and the sensor dimensions. Any FOV values given in lens specs are just meant as a convenience for the reader, but can easily cause confusion if the user's sensor isn't identical to the one assumed in the lens spec.

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The sensor is a Full-HD one, natively giving 1920 * 1080 resolution. If used in 720P mode (1280 * 720), it will most probably still use the full sensor size, and only digitally reduce the resolution, effectively simulating larger pixels of 4.35µm. So, this does not change the FOV calculation, as still the full sensor dimensions are in use.

Plausibility check: according to Wikipedia on image sensors, your 1/2.8" sensor should have a diagonal between the listed 1/2.9" and 1/2.7" formats, i.e. between 6.23mm and 6.72mm. So, the calculation above, based on the pixel size, seems correct.

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