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## Questions

### Subject:Trigonometry

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Question:

Calculate sin(-585°).

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sin(-585°) = sin(585°) [sin(-a) = sin(a) = sin(2π+225°) [585 = 360 +225] [360 = 2π] = sin225° [sin(360 + a) = sin(a)] = sin(π+45°) [225 = 180+25] [180 = π] = sin45° [sin(180 +a) = sin(a)]

### Subject:Discrete Math

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Question:

Let p and q be propositions: p = “you get an A on the final exam” q = “you do every exercise in this book” r = “you get an A in this class” Write the following propositions using p, q, and r and logical connectives. 1. To get an A in this class it is necessary for you to get an A on the final. 2. Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class.

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1. p --> r 2. (p AND q) --> r

### Subject:Artificial Intelligence

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Question:

What is a breadth-first search Strategy?

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A Search strategy, in which the highest layer of a decision tree is searched completely before proceeding to the next layer is called Breadth-first search (BFS). In this strategy, no viable solutions are omitted and therefore it is guaranteed that an optimal solution is found. This strategy is often not feasible when the search space is large The following BFS Algorithm can be implemented in any programming language Create a variable called LIST and set it to be the starting state. Loop until a goal state is found or LIST is empty, Do Remove the first element from the LIST and call it E. If the LIST is empty, quit. For every path each rule can match the state E, Do Apply the rule to generate a new state. If the new state is a goal state, quit and return this state. Otherwise, add the new state to the end of LIST Advantages Guaranteed to find an optimal solution (in terms of shortest number of steps to reach the goal). Can always find a goal node if one exists (complete). Disadvantages High storage requirement: exponential with tree depth

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