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1、09IB04 32 Graph of Sine & CosineThis is Mr. Hu on a paradise island called “Guam” in the Pacific Ocean.Review with unit circle:Graph of Sine and Graph of Sine and Cosine FunctionCosine FunctionObjectives:Objectives:Students will be able to sketch the curves of basic Students will be able to sket
2、ch the curves of basic sine and cosine functions.sine and cosine functions.Students will be able to identify the amplitude and Students will be able to identify the amplitude and fundamental period of sine and cosine functions.fundamental period of sine and cosine functions.Students will be able to
3、sketch translations of Students will be able to sketch translations of graph of sine and cosine functions.graph of sine and cosine functions.Since sine ratio of is y/r, in unit circle where r = 1, sin= ysin is an odd function because sin(-) = -sin. And, its period is 2 because it starts to repeat th
4、e same ratio over again for every 2 radians. Its rotation goes on forever. So, its domain is all real number. And, its range is -1 y 1.Since cosine ratio of is x/r, in unit circle where r = 1, cos= xcos is an even function because cos= cos(-). And, its period is 2 because it starts to repeat the sam
5、e ratio over again for every 2 radians. Its rotation goes on forever. So, its domain is all real number. And, its range is -1 y 1.Compare to the graph of y = sin x, curve of y = cos x is the curve of y = sin x shifted /2 to the left. Key Points in the Sine and Cosine CurvesThe amplitude “a” of f(x)
6、= a sin x or f(x) = a cos x is the half the distance between the maximum and minimum values of the function.The fundamental period “p” of periodical function f(x) is the smallest positive number such that f(x + p) = f(x).For f(x) = sin bx or f(x) = cos bx, p = 2/ b.Example: GraphAmplitude:Period:Key points:Another Example:GraphVertical shift:Horizontal shift:Key points:Amplitude:Period:Assignment 22Page 304-307Item# 1, 4, 7, 10, 13, 17, 20, 23, 24, 25, 26, 29, 32, 33, 35, 37, 41, 44, 49, 50, 55, 56, 60.
