Every Australian school kid from my generation knows the basics of the Captain Cook story, though we were always told the important bit was the discovery of Australia's east coast.
So let's start with that one.
The chief purpose of Cook's first voyage was observing the transit of Venus from Tahiti, and once he'd done that his orders were to have a look around the Pacific Ocean and see if he could lay eyes on the great southern continent that many highly rated geographers assumed must be there because the northern hemisphere was so land heavy and all they'd managed to find south of the equator was the southern part of Africa, a fair chunk of the Americas, and this stretch of New Holland the Dutch had run across that we now know as Western Australia, Arnhem Land, the western side of Cape York and the Gulf of Carpentaria.
There must be another substantial chunk of land down there. It was just that no one had so far managed to bump into it.
That explains the path Cook followed between leaving Tahiti and circumnavigating New Zealand. It was more a less a case of let's see if it's over here.
Abel Tasman had sailed along the western coast of New Zealand, and proved New Holland didn't stretch that far east, so Cook's next job was to show how far east New Zealand went. He did a figure of eight around the Shaky Isles, decided it obviously wasn't the Great South Land and headed for the continent we now know as Australia.
All of which explains why he was sailing along the east coast. He was doing what he would have done if he'd run across anything that hadn't been charted already. Head over to the Wikipedia entry for James Cook and you can see what he was up to, particularly on his second voyage (the green line on the map) which was his attempt to sink the assumptions about this Great Southern Land once and for all.
In any case, while he was being careful sailing along the north Queensland coast he wasn't being careful enough, struck coral off Cape Tribulation, and went within an inch of losing the whole kit and caboodle. He managed to get the Endeavour off the reef, fostered the hole in the hull with a spare sail and made for land, finding an ideal anchorage in what we now know as the Endeavour River.
Whether he had a copy of the sixteenth century maps that presumably report Portuguese discoveries and labels the area around Cape Tribulation as Coste Dangeureuse or been briefed about it is something that seems to have been left out of the standard accounts, and there’s a strange remark in his Journal:
this harbour will do excellently for our purposes, although it's not as large as I had been told.
Cook, of course, could have been given this information by the lookout in the crow’s nest or a boat crew.
The old Queensland Social Studies Book had a brief reference to difficulties with the locals, but the gist of the rest of the story was he patched up his ship, made it home and received great acclaim for discovering what he had labelled New South Wales.
The reality was that he'd observed the Transit of Venus (good job, well done), failed to find the Great South Land (well where it it, then?) and, most significantly for a voyage of that length, failed to lose a man through scurvy (that's vitamin C deficiency in case you haven't run across the term before).
For most of the European seagoing community, and particularly for the Royal Navy this was pretty big news. Far bigger news, in fact, than the charting of the eastern chunk of something we already knew was there.