Answer based on context:

The squadron of Vasco da Gama left Portugal in 1497, rounded the Cape and continued along the coast of East Africa, where a local pilot was brought on board who guided them across the Indian Ocean, reaching Calicut in western India in May 1498. The second voyage to India was dispatched in 1500 under Pedro Álvares Cabral. While following the same south-westerly route as Gama across the Atlantic Ocean, Cabral made landfall on the Brazilian coast. This was probably an accidental discovery, but it has been speculated that the Portuguese secretly knew of Brazil's existence and that it lay on their side of the Tordesillas line. Cabral recommended to the Portuguese King that the land be settled, and two follow up voyages were sent in 1501 and 1503. The land was found to be abundant in pau-brasil, or brazilwood, from which it later inherited its name, but the failure to find gold or silver meant that for the time being Portuguese efforts were concentrated on India. On 8 July 1497 the fleet, consisting of four ships and a crew of 170 men, left Lisbon The travel led by Vasco da Gama to Calicut was the starting point for deployment of Portuguese in the African east coast and in the Indian Ocean. The first contact occurred on 20 May 1498. After some conflict, he got an ambiguous letter for trade with the Zamorin of Calicut, leaving there some men to establish a trading post. Since then explorations lost the private nature, taking place under the exclusive of the Portuguese Crown. Shortly after, the Casa da Índia was established in Lisbon to administer the royal monopoly of navigation and trade.

Which ocean did Da Gama cross?
Indian Ocean