Why did Cook navigate the east coast of Australia?

Answer 1

He didn't: he claimed it for England. Because James Cook was English, he claimed the eastern half of the Australian continent for England, and named it New South Wales. The Dutch had named the western half New Holland, but not claimed it. The British sought to expand their Empire, and they could only do this by claiming lands which no other country had yet claimed.

Answer 2

Australia was regarded as Terra Nullius which means "land that belongs to no-one".

This applied to Australia because the British did not recognise that the indigenous people of Australia were the rightful "owners" of the land. Because the Aborigines were seen as little more than black savages, the British considered that Australia belonged to no-one and that it was within their right to claim the land as their own, and to do with it (and its people) whatever they wished.

Answer 3

James Cook was under secret orders to try to find the great unknown southern continent, and claim it for Britain. He navigated the coast because he was required to chart the eastern coastline of what he called "New South Wales" (now Australia), make extensive notes on the people, flora, fauna and prospective suitability for colonisation, and report back to England.