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Bowing evolved as a traditional sign of respect and acknowledgement in many Western cultures, but it is much less common than it once was. You may still bow to show respect, or to add a dramatic flourish to a situation, but the gesture will appear a bit outdated. That said, bowing is still generally regarded as a polite gesture.  Bowing in western culture is often accompanied by an air of mock formality, and perhaps a degree of ironic self-consciousness. The European-American ceremonial bow is largely an anachronistic gesture, so bear in mind that you may not be taken seriously. Try owning the mock formality of the bow by playing with nuance and taking the gesture to the extreme. Bow very slowly and deeply to show sarcasm—something like a slow clap. Bow very quickly and politely to convey mock deference. Bend your arm at the elbow, and rest your hand (palm out( at waist-level. Alternately, press your left hand across your abdomen. Bend your arm at the elbow. Hold your palm against your body while you tip your upper body forward. The lower you bend, the more respect you show. If you are wearing a hat, remove it and hold it by the brim in your right hand. If you are in a situation that calls for extreme deference—say, a funeral, or the performance of a national anthem—tuck your hat under your arm until the moment passes. Do not raise your chin to maintain eye contact—this may be taken as a sign of disrespect. This is, however, a tradition that evolved from a highly stratified feudal society, so do not expect most 21st-century people to take offense if you make eye contact or bow "incorrectly". Straighten your back. Drop your hands. Raise your eyes to meet the gaze of the person to whom you bowed, and proceed to speak with them.
Know when to bow. Put your left hand behind your back. Bring your right hand to your waist. Keep your eyes lowered. Stand up in one fluid motion.