These three words all sound alike but are often misused.
PEEK means to sneak a glance, usually furtively. Adam peeked in the attic where the Christmas presents were stored.
PEAK is the apex of something: the top of a mountain, a gable on a house, the points on egg whites when they are whipped hard.
PIQUE as a noun is a feeling of annoyance, especially if one’s pride or honor is insulted.
PIQUE as a verb means to stimulate interest: A review of Ian McEwan’s latest book, Nutshell, piqued my interest in reading it. It is an achingly clever novel narrated by a full-term fetus (unnamed, but obviously a modern-day Hamlet, whose mother is Trudy, father is John, and doltish uncle and Trudy’s lover is Claude).