How are cellular respiration and photosynthesis part of the carbon cycle?

Respiration takes place in almost all living things (some bacteria get their energy from the break down of sulfur compounds in deep ocean vents.) In respiration glucose sugar # C6H12O6# is broken down into 6 Carbon Dioxides (#CO2#) and 6 Waters (#H2O#)

Respiration is an oxidation reaction producing energy. The respiration equation requires 6 oxygen molecules (#O2#) This energy is usually used to produce ATP

The complete equation is
1 #C6H12O6# + 6 #O2# == 6 #CO2# + 6 #H2O#

Photosynthesis takes place only in green plants. Photosynthesis is an endothermic reaction it requires the energy from sunlight to push the reaction forward.

Photosynthesis is the exact opposite of Respiration. Just take the respiration equation and turn it around.

6 #CO2# + 6 #H2O# === 6 #O2# + 1 #C6H12O6#

Respiration produces Carbon Dioxide and Photosynthesis uses Carbon Dioxide to produce Glucose a Carbon compound.

(Note Oxygen is a by product of photosynthesis but is necessary for almost all life both plants and animals need oxygen for life.)