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Chapter 6: Q. 13 (page 437)

Find a sinusoidal function for the following graph.

Short Answer

Expert verified

The sinusoidal function for given graph is :y=3cosx2or3sin蟺2-x2

Step by step solution

01

Step 1. Given information 

02

Step 2. Assume the graph equation   

This shown graph shows the characteristics of the cosine function, it is symmetric about the y-axis

so let's assume the graph like

y=Acos蝇x

from figure

amplitude A=3

period T=12

03

Step 3. calculating the ω

We know that T=2蟺蝇

12=2蟺蝇蝇=蟺6

so,the cosine function is,for amplitude 3 and蝇=蟺6is

y=3cos蟺6xor3sin蟺2-蟺6x

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