He was one of four members of the Latvia-Taiwan parliamentary cooperation group, which was touring China on a mission to discuss trade and human rights.
As leader of a Tibet support group in Latvia, Sinka was involved in arranging a visit by the Dalai Lama to Latvia, to take place this June. China has ruled Tibet with an iron fist to control separatist sentiment since occupying the region in 1950.
Following the announcement a framed photo of Sinka was hung in the entrance to Latvia's Parliament building, above a table draped in black, on which stood flowers and a burning candle.
President Vaira Vike-Freiberga issued a statement praising Sinka.
"We have lost a man who devoted all his efforts to the idea of a free Latvia and the maintenance of its good name, throughout his years in exile and in the years since independence was restored," she said.
Sinka fled to Britain as a teenager when Latvia was occupied by the Soviet Union at the end of World War II. He studied politics, economics and philosophy at Oxford University and then worked for the British Broadcasting Corporation monitoring Soviet radio at Caversham Park in southern England. He also taught Russian in evening classes. In 1988 he moved to Germany, becoming editor of the Latvian exile newspaper Free Latvia.
Returning to Latvia when he was elected to the Parliament in 1993, Sinka was known for his tough stance toward the Russian-speaking community. He also defended the reputation of the controversial Latvian Waffen SS, known locally as the Latvian Legion, which fought on the German side against Soviet forces following Latvia's occupation by Germany in 1941.
A close colleague, MP Palmira Lace, said: "He was the only exile MP who held the national line and knew what the Russians had done. Latvia has lost an irreplaceable patriot in the mountains of Tibet."
Others praised Sinka's defense of threatened nations around the world. As chairman of Latvia's delegation to the Council of Europe he spoke out against Russia's conduct of its war in Chechnya.
Latvia's Way MP Peteris Apinis, who was with Sinka in Tibet, said his efforts to resuscitate him in his hotel room came too late.
"Despite suffering from shortness of breath he had refused to miss any of the schedule," said Apinis. "In private Sinka was a revolutionary, but with the Chinese authorities he was a very good diplomat. He devoted his life to bringing democracy to the world and he died in his efforts. He was a real democrat."
Sinka raised eyebrows last autumn when he penned new words to Russia's czarist-era anthem in response to the reintroduction of the Soviet tune approved by Stalin. He sent his version to the Paris-based Russian newspaper Russian Thoughts. "My words are perfectly serious and inspiring," he told The Baltic Times.
Sinka is survived by his wife Maija, and two children, Indra and Aivars, by a previous marriage. A memorial service will be held at 10 a.m. on April 17 in Riga's Dome Church, followed by his burial at the First Meza cemetery.