Half-Wave Design: Find Sine Function y=asin(b(x-c))+d

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SUMMARY

The half-wave design can be accurately modeled using the sine function in the form y=asin(b(x-c))+d. The correct representation derived from the discussion is y=4sin(π/10(x+5))+7, where the amplitude is 4, the frequency is π/10, the phase shift is -5, and the vertical shift is 7. The domain for this function is defined as x between -5 and 5, which is crucial for accurately depicting the half-wave design.

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  • Understanding of sine functions and their properties
  • Knowledge of amplitude, frequency, phase shift, and vertical shift
  • Familiarity with the equation format y=asin(b(x-c))+d
  • Basic skills in graphing functions
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Homework Statement


The half-wave design may be represented as a portion of a sine function. Determine a sine function that models the half wave design, assuming that the origin is at the point (0,0). Express in the form y=asin(b(x-c))+d
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Homework Equations


y=asin(b(x-c))+d


The Attempt at a Solution


My answer is y=4sin(\frac{\pi}{10}(x+5))+7

Am I right? I was just confused when the question said to represent it as a portion of a sine function.
 
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The function is fine, you just need to define a domain for the half-wave design.
 
Thanks. I forgot to write it down, but the question already provides the domain of x between -5 and 5.
 

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