Explanation:

• The Trinity of Carnatic music, also known as The Three Jewels of Carnatic music, refer to the outstanding trio of composer-musicians of Carnatic music in the 18th century, being Tyagaraja, Muthuswami Dikshitar and Syama Sastri. Compositions of the Trinity of Carnatic music are  recognized as being distinct in style, and original in handling ragas. They were patronised and supported by  the king of Tanjore.
• Tyagaraja (1767 - 1847): Tyagaraja composed thousands of devotional compositions, most in Telugu  and in praise of Lord Rama, many of which remain popular today. Of special mention are five of his compositions called the Pancharatna Kritis which are often sung in programs in his honour. Tyagaraja saw the reigns of four kings of the Maratha dynasty — Tulaja II (1763–1787), Amarasimha (1787–1798), Serfoji II (1798–1832) and Sivaji II (1832–1855), although he served none of them.
• Muthuswami Dikshitar (1775 - 1835): His compositions, of which around 500 are commonly known, are noted for their elaborate and poetic descriptions of Hindu gods and temples and for capturing the essence of the raga forms through the vainika (veena) style that emphasises gamakas. They are typically  in a slower speed (chowka kala). He is also known by his signature name of Guruguha which is also his mudra and can be found in each of his songs. He visited and composed ragas at the temples at Kanchi, Tiruvannamalai, Chidambaram, Tirupathi and Kalahasthi, Srirangam, before returning to Tiruvarur.
• Shyama Shastri (1762–1827): Shyama Shastri adopted common as well as rare ragas for his compositions. Though his compositions were in three languages - Tamil, Telugu, and Sanskrit - he preferred Telugu as the medium of expression. He is the only one among the ‘Trinity’ to have composed in Tamil. Shyama Shastri signed his compositions - Kritis, Var?am(s) and Swarajati(s) with his Mudra (Signature) ‘Shyama Krishna’. He was sponsored and supported by the king of Tanjore.
• Annamayya (1408 - 1503) was a 15th-century Hindu saint and is the earliest known Indian musician to compose songs called sankirtanas in praise of the god Venkateswara, a form of Vishnu. He is the first known composer in carnatic music. Other composers likePurandaradasa came after him. The musical form of the keertana songs that he composed, which are still popular among Carnatic music concert  artists, have strongly influenced the structure of Carnatic music compositions. He saw the reign of Vijayanagar kingdom under the rule of Saluva Narasimha Raya