cycle
The word 'cycle' in French is the same as in English. It is used to describe a series of events that are regularly repeated in the same order. For example, 'the cycle of the seasons' or 'the life cycle of a butterfly'.
I use my bike to do the cycle to work every day.
In this sentence, 'cycle' is used to mean 'route' or 'journey' as in the daily commute to work. In French, the same word 'cycle' as in English is used, but it is more commonly used to refer to a bicycle rather than a route or journey. The 'du' in 'cycle du travail' is used as 'to' in English. So 'cycle du travail' literally translates to 'cycle to work'.
The water cycle is an important natural phenomenon.
In this sentence, 'cycle' is used to refer to 'the water cycle', an important concept in Earth science. Just like in English, in French 'le cycle de l'eau' refers to the continuous movement of water on, above, and below the surface of the Earth.
He is in a deep sleep cycle.
In this sentence, 'cycle' is used to refer to 'a sleep cycle', which is a part of the human circadian rhythm or natural sleep-wake cycle. In both English and French, 'cycle de sommeil' refers to one of the several repeating sleep stages a body goes through during sleep.