cos([theta] + [alpha]) = 1/2 sin (theta) = -1/2 Find all possible values for Theta and Alpha
arcsin (-1/2) = (11pi)/6 or (7pi)/6 If Theta = (11pi)/6 cos((11pi)/6 + alpha) = 1/2 Alpha = - pi/6 or (3pi)/6 If theta = (7pi)/6 cos((7pi)/6 + alpha) = 1/2 alpha = (3pi)/6 or -(5pi)/6
Which branch of government is the weakest and why?
The weakest branch of the government is the judiciary. It lacks the power of the sword which is the domain of the executive, and it lacks the power of the purse which is that of the legislature. It cannot enforce it's own ruling now can it act proactively; it must always be a responsive body. It is most cases, not elected but appointed and thus is structurally beholden to the other branches of government. Finally, it is institutionally weak because it requires the compliance of the other two branches to effect it's rulings and insure that they are carried out as intended.
The framers had to deal with many competing interests in drafting the US constitution? Briefly discuss three sets of competing interests that the framers dealt with and one way they tried to compromise for each set.
They tried to balance tyranny against effective governance, states rights against national prerogatives, and popular representation against mob rule. - The framers were concerned about how they could make a government that could address issues that the Articles of Confederation government could not. Alexander Hamilton especially understood the need for an "energetic executive" (Fed. Papers 76-77) which could effectively deal with problems in times of crisis. However, other framers were afraid of a strong executive which they felt would inevitably become an american tyrant and destroy the democratic system. The compromise between these positions was a system of checks and balances designed to promote effective government while preventing any one branch from becoming tyrannical. - The framers also worried about balancing the rights of small rural states against the federal government which would be controlled by exterior forces from other states. However, they also didn't want to have an ineffective government forced to kneel to the interests of small factions. Under the Articles of Confederation, the legislature needed a unanimous vote to accomplish anything which allowed small factions to control the course of the whole nation. The solution to this problem was a federal system of separated powers. Under this system the states and the national government would divide power between themselves such that both the state and national governments could accomplish what they needed to. - Finally the framers were worried about democracy itself as a system. The framers were, contrary to popular perception, an incredible elitist group composed of a class of american aristocrats—landholders, slaveowners, businessmen, children of wealth. As a result they had an immense distrust of the people's capacity to actually govern effectively because they believed that most of the voting base was incapable of making good decisions for themselves. In order to deal with this they created the electoral college. The Electoral college was a system whereby the president is elected by a board of electors from each state. This would provide a veto point where the electors, who were political elites, could change the outcome of an election if they disapproved of the choice made by the citizens of each state.