What were two movements that emerged in American society during the 1830s and 1840s that dealt with the connection between Evangelical Protestantism and the reform movements? What were the movements trying to accomplish and how did they go about it?

One movement with explicit connections to Evangelical Protestantism was the abolitionist movement. While the issue of slavery divided most of the main Protestant denominations, Evangelicals were at the vanguard of the movement in the North. Quakers had long opposed slavery, frequently petitioning the federal government against the institution and advocating emancipation in Northern states. William Lloyd Garrison, perhaps the most vocal abolitionist other than Frederick Douglass, was motivated in large part by his belief that slavery was a sin that could not be tolerated by American Christians. Others like the Grimké sisters and Wendell Phillips were also motivated by their religious beliefs, as were two men who attempted to launch slave revolts in Virginia—Nat Turner and later John Brown.
Evangelicals also railed against the evils of alcohol in what was known as the temperance movement. Across the nation, Evangelical preachers railed against the evils of alcohol, which they painted as a great source of evil in American society. Lyman Beecher, the founder of the American Temperance Society, was a Presbyterian minister who spent much of his life preaching against alcohol from the pulpit. In town after town in the North, especially the Northeast and Ohio, congregations took "teetotal pledges" to avoid all alcohol.
In general, Evangelicalism, which arose with the Second Great Awakening, helped spark all of the major reform movements, including abolition and temperance, in the 1830s. People began to envision a society shaped by Christian virtue and to believe that sins could be purged from society.
http://nationalhumanitiescenter.org/tserve/nineteen/nkeyinfo/amabrel.htm

https://ohiohistorycentral.org/w/Lyman_Beecher