Dang homophones. They sound the same, aren't always spelled the same, and always mean different things. I've seen this particular set mixed up every-which-way, when, in fact, they have completely different (not even close!) meanings.
Peek: to look at something stealthily. I took a peek in that box. Eek! There was a mouse!
Peak: the top or pinnacle of something. We hiked to the peak. Or, He was at the peak of his fitness.
Pique: (verb) to arouse interest. My curiosity was piqued.
The most common offender tends to be seeing peak when peek is meant (as in take a peak). Whenever I see this, I visualize someone offering me peaks of stiffly whipped cream or handing over the deed to a mountain. You can avoid this error by remembering if you take a peek, you might say Eek! (Get that? The "Eek" is the last three letters of "peek"? ...Okay, it's dorky, but sometimes dorky works.)
Though it is possible for your curiosity to peak (as in, reach the highest levels it ever has), it's generally more common that your curiosity is piqued (as in, something arouses your interest).
To showcase your new knowledge, you can try to slip this sentence in somewhere:
My interest was piqued after taking a peek at that peak.