Final answer:
The 16th and 17th Amendments to the U.S. Constitution were passed under President William Taft in 1913. These amendments allowed for the federal income tax and for the direct election of U.S. Senators, respectively.
Step-by-step explanation:
The 16th and 17th amendments were passed under the presidency of William Taft. The 16th Amendment, which allows Congress to levy an income tax without apportioning it among the states or basing it on the United States Census, was passed in 1913. Similarly, the 17th Amendment, which established the direct election of U.S. Senators by popular vote, was also ratified in 1913.
Progressives were greatly responsible for lobbying for democratic reforms including the 17th Amendment, aiming to achieve fairer representation in Congress and reduce corruption associated with the previous system of state legislatures appointing senators. William Jennings Bryan was amongst the key figures advocating for this change. While the Progressive movement influenced both amendments, the actual passage occurred during President Taft's administration, before Woodrow Wilson took office.