Audacity, as mentioned is the best free option.
There is also REAPER, which is $60, although you can actually use the trial indefinitely.
Why do you need to record yourself playing trombone? Most of the time, brass instruments won't sound good, almost at all with a laptop microphone.
Really, if you get audacity, and get a good USB mic, such as a YETI Blue, you will be spending on the mic that will sound good for most purposes, and have a good recording program to use.
Can Anyone recommend a good recording program for PC? I have to record myself playing my trombone.
Garage Band and Tonal Energy don't work on PC. I have a Real Teck microphone in my laptop, so what would work with it?