Use interval notation to represent the domain and range of the following functions. hint: start by thinking about the meaning of each function's input and output quantities and the values those quantities can assume. determine the domain and range of the cos − 1 function. domain: range: determine the domain and range of the sin − 1 function. domain: range: determine the domain and range of the tan − 1 function. domain: range:

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

If angle b measures 25°, what is the approximate perimeter of the triangle below? 10.3 units 11.8 units 22.1 units 25.2 units

Use the given information to determine the exact trigonometric value.