I just started playing Tristana a few days ago and she is quickly becoming my favorite adc. I have been wondering, though, why no one takes trinity force on her. I mean, she has ap ratios, it seems fairly logical. I'd just like to know the reasoning behind why she doesn't use it. Ty
Insanely high cooldowns If I'm correct, all her cds are like 15 seconds excluding her ult
Trinity Force has 2 main parts. Sheen is for procing castable adcs (like Ezreal/Corki). Tristana is not going to be able to cast as much (Ezreal Q/Corki R) and her W and R are disengage friendly which means she won't be able to auto after it.
Lastly Trinity Force naturally makes you tankier which Tristana does not need due to her range. Trinity Force is a viable option for any adc, especially those who are scared of being jumped by heavy dps but she does not utilize it as effectively.
If you are picking it solely because she can utilize the AP it gives, then that's a bad reason to choose it. on Trist, you want to capitalize on a few key things: High AS for DPS and faster E stacking, and high AD for more E damage and tower killing. Throw in som crit and you're all set. Trinity force is super expensive and she doesn't utilize or really need a lot of what it gives (AD AS and Crit are decent, but she rarely uses the sheen proc, and doesn't need the mobility it offers, and the health and mana are pretty underwhelming).
Because 
only gives 30 AP. 30 more damage on an ultimate and around 20 to two other skills is really negligible. The passive doesn't work too well with her since her cooldowns aren't ridiculously low or used as AA resets like 
or 
to proc it.
