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Unformatted text preview: Graphs of the Sine and Cosine Functions Comments Since both sine and cosine are periodic functions, it is enough to learn the basic shape of the graph for one period. To graph over an interval of length more than one period, the basic graph is repeated as many times as needed. Characteristics of the Sine Function • Domain: all real numbers • Range: [1, 1] • Period: • Maximum value: 1 at • Minimum value:  1 at • Odd function: graph symmetric with respect to the origin • xintercepts: • yintercept: (0, 0) π 2 n x π π 2 2 + = n x π π 2 2 3 + = integer any n ), , (n π The Graph of y = sin x, period 6 3 2 5 6 3 2 2 π π π π π π π 1 2 3 2 1 1 2 1 x y π 2 2 4 6 1.5 1.5 (0, 0) ( 29 π 6 1 2 , ( 29 π 2 1 , ( 29 π ,0 ( 29 3 2 1 π , ( 29 2 π , Definition The amplitude of a periodic function with minimum value m and maximum value M is 2 m M A = Hence, the amplitude of the sine function is 1 2 2 2 ) 1 ( 1 = = = A Characteristics of the Cosine Function • Domain:...
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This note was uploaded on 01/22/2011 for the course MATH 2 taught by Professor Gardner during the Fall '08 term at Irvine Valley College.
 Fall '08
 GARDNER
 Calculus, PreCalculus

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