Pre-Calc Exam Notes 109

# Pre-Calc Exam Notes 109 - Properties of Graphs of...

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Properties of Graphs of Trigonometric Functions Section 5.2 109 5.2 Properties of Graphs of Trigonometric Functions We saw in Section 5.1 how the graphs of the trigonometric functions repeat every 2 π radi- ans. In this section we will discuss this and other properties of graphs, especially for the sinusoidal functions (sine and cosine). First, recall that the domain of a function f ( x ) is the set of all numbers x for which the function is de±ned. For example, the domain of f ( x ) = sin x is the set of all real numbers, whereas the domain of f ( x ) = tan x is the set of all real numbers except x = ± π 2 , ± 3 π 2 , ± 5 π 2 , .... The range of a function f ( x ) is the set of all values that f ( x ) can take over its domain. For example, the range of f ( x ) = sin x is the set of all real numbers between 1 and 1 (i.e. the interval [ 1,1]), whereas the range of f ( x ) = tan x is the set of all real numbers, as we can see from their graphs. A function
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