Dangerous Sorcery says I get bonus damage "When you Cast a Spell from your spell slots". While cantrips don't expend slots when you cast them, do you still get a bonus from Dangerous Sorcery when casting a cantrip?
The very first line for the rules for Cantrips in the Sorcerer class says
A cantrip is a special type of spell that doesn’t use spell slots.
Seems pretty cut and dried - Cantrips don't use spell slots, so wouldn't get the bonus.
The other answers have laid it out pretty clearly. Cantrips don't cast from spell slots, and therefore don't qualify. This is deliberate. The "from your spell slots" caveat is there specifically to prevent the use of that power with cantrips (or with anything else that might let you cast the spell without burning a slot).
In general, every bit of rules text has a purpose. There are products that are poorly-written, where this is not always true, but Paizo core rulebooks are usually pretty good about that sort of thing. If you're looking at a bit of rules text and cannot figure out if it applies to your specific case, one of the first questions to ask is what else it might mean. If there's no other clear thing that it could be referring to, your case is probably it.
To add to other answers, if there's a spell which allows you to use a cantrip you don't usually have such that the result is a spell slot being consumed while a cantrip is also cast, then I'd say that Dangerous Sorcery should apply.
I'm not sure which spells can use this but my DM has homebrewed some "temporary knowledge of a cantrip" for our Sorceror, because it works so well with quickened-spell for enabling some tricky problem solving, whilst also consuming spell slots + sorcery points, ensuring it's only used sparingly and doesn't just result in a "caster with ALL the cantrips!".
Our campaigns feature lots of magic items with single-use or few-use low-power spells. This is pretty much the same as homebrew, limited use cantrips for us.