EXPLORING DATA AND STATISTICS Modeling with 14

Page 1 of 2862 Chapter 14 Trigonometric Graphs, Identities, and EquationsModeling withTrigonometric FunctionsWRITING ATRIGONOMETRICMODELG raphs of sine and cosine functions are called sinusoids. When you write a sine orcosine function for a sinusoid, you need to find the values of a, b>0, h, and kfory= a sin b(x h) + kor y = a cos b(x h) + kwhere |a| is the amplitude, 2b is the period, h is the horizontal shift, and kis thevertical Trigonometric FunctionsWrite a function for the the maximum and minimum values of the function occur at pointsequidistant from the x-axis, the curve has no vertical shift. And because theminimum occurs on the y-axis, the graph is a reflection of a cosine curve with no horizontal shift. Therefore, the function has the form y= period is 2b = 23 , so b= amplitude is |a| = 4. Since the graph is a reflection, a= 4. The function is y= 4 cos the maximum and minimum values of the function do notoccur at pointsequidistant from the x-axis, the curve has a vertical shift.

Page 1 of 2 14.5 Modeling with Trigonometric Functions 863 Modeling a Sinusoid Write a trigonometric model for the average daily temperature in Birmingham, Alabama. Source: National Climatic Data Center

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