The second trump is mentioned in both the Doctrine and Covenants and the book of Revelation. In the Doctrine and Covenants, it signals the resurrection of the terrestrial beings (see D&C 88:99). The first trump speaks of the celestial resurrection. The third and fourth trumps speak of the assigning of spirits of telestial beings and sons of perdition to the spirit world for one thousand years (see D&C 88:96–102). In the book of Revelation, the first through the fourth angel speak of the destruction of various parts of the earth and changes to the sun and the moon (see Revelation 8:6–13). Therefore, there is no correlation between the angels mentioned in the Doctrine and Covenants and the book of Revelation. The book of Revelation is describing the destruction of the telestial beings from the earth in preparation for the Second Coming. The other two parts that are not destroyed are the celestial and terrestrial beings. This interpretation is supported by the revelation given to Joseph Smith explaining the book of Revelation.
Q. What are we to understand by the sounding of the trumpets, mentioned in the 8th chapter of Revelation?
A. We are to understand that as God made the world in six days, and on the seventh day he finished his work, and sanctified it, and also formed man out of the dust of the earth, even so, in the beginning of the seventh thousand years will the Lord God sanctify the earth, and complete the salvation of man, and judge all things, and shall redeem all things, except that which he hath not put into his power, when he shall have sealed all things, unto the end of all things; and the sounding of the trumpets of the seven angels are the preparing and finishing of his work, in the beginning of the seventh thousand years—the preparing of the way before the time of his coming. [D&C 77:12]
The sanctifying of the earth and the completion of the salvation of man will include the destruction of the wicked or the telestial beings from the earth. This work of destruction will be cut short by the teaching of the gospel to as many as will hear his voice. This interpretation is also supported by modern revelation.
94 And another angel shall sound his trump, saying: That great church, the mother of abominations, that made all nations drink of the wine of the wrath of her fornication, that persecuteth the saints of God, that shed their blood—she who sitteth upon many waters, and upon the islands of the sea—behold, she is the tares of the earth; she is bound in bundles; her bands are made strong, no man can loose them; therefore, she is ready to be burned. And he shall sound his trump both long and loud, and all nations shall hear it.
95 And there shall be silence in heaven for the space of half an hour; and immediately after shall the curtain of heaven be unfolded, as a scroll is unfolded after it is rolled up, and the face of the Lord shall be unveiled;
96 And the saints that are upon the earth, who are alive, shall be quickened and be caught up to meet him. [D&C 84:94–96]
The context of the Mosiah verses above fit into this explanation.