Man and shark — most experts agree we can coexist peacefully with the oceans’ most notorious predator but in practice it hasn’t always worked out that way.

Two documentaries airing this week during Discovery’s 29th annual Shark Week, which began June 26 and runs through July 3, illustrate the ups and downs of this most tenuous of relationships.

“Sharks Among Us,’’ airing Monday at 10 p.m., details how encounters with sharks are on the rise and so is public anxiety. The easy answer, some say, is to kill sharks through either culling and netting. But others, among them marine biologist Craig O’Connell, say there is another way. He has come up with a system that he believes will allow us to live together peacefully.

Most shark attacks are cases of mistaken identity. The usual scenario is a surfer in a wet suit on a surfboard, arms and legs splayed and paddling, which from below looks like the shark’s natural prey, a seal. It’s not all that dissimilar to throwing a bass spoon or a Rapala minnow at a smallmouth bass. Sooner or later, they’re going to bite.

Paul de Gelder, a former Australian Navy clearance diver, found himself on the wrong end of one of these encounters. In 2009, an attack by a 9-foot bull shark left him without a right leg and hand. Initially terrified of sharks, the incident led him to face his fears and eventually develop a passion for sharks. Today, he’s a motivational speaker, adventurer and mentor to schoolchildren.

On the flip side, there is man’s devastation of the shark population. One of the most notorious cases, as detailed in “Nuclear Sharks’’ on Thursday, are the multiple tests of nuclear bombs in the South Pacific from 1946-58. The multiple explosions left Bikini Atoll and nearby islands devastated and bereft of life, including sharks. Now, 70 years later, the islands are lush though still uninhabitable because of cesium in the soil, and reef sharks have returned to the area. Unfortunately, so has an illegal shark-finning operation.

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Still, the show’s co-producer, underwater explorer and filmmaker Philippe Cousteau, was heartened.

“Nature has an incredible ability for resilience and renewal,’’ Cousteau says. “Because people oftentimes ask me, you know, the oceans are in such a bad way in many cases, what can we do about it? I mean, is there any hope? And I think that ‘Nuclear Sharks’ really proves there is hope, that nature can renew.”