I used to work and hunt where there were plenty of cougars in the Cascades. Never saw one but a mountain biker was killed by one not far from here about a year ago. The fact is you just hardly ever see them.
Just about any pistol cartridge will work to kill a cougar. I used to carry a 357 revolver when I could. Employers policy was no firearms so I carried a machete. Kept a razor edge on it too. I hate hiking in the mountains around here unarmed. Actually I hate going anywhere around here unarmed.