Phase shift and sinusoidal curve fitting - Finding .

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SUMMARY

The discussion focuses on determining the period, amplitude, and phase shift of the sinusoidal function y = 4sin(2x - π). The amplitude is established as 4, and the period is calculated to be 2. The phase shift is identified as π/2. Participants emphasize the importance of graphing the function accurately by plotting points in increments of 0.1 radians over the interval from 0 to 2π radians, and then extending the plot back to -π radians for a complete representation.

PREREQUISITES
  • Understanding of sinusoidal functions and their properties
  • Knowledge of amplitude, period, and phase shift concepts
  • Familiarity with graphing techniques using graph paper
  • Basic skills in using a calculator for trigonometric functions
NEXT STEPS
  • Learn how to calculate the interval defining one cycle of a sinusoidal function
  • Research the concept of subinterval width in graphing
  • Explore advanced graphing tools like Desmos for visualizing sinusoidal functions
  • Study the effects of varying amplitude and frequency on sinusoidal graphs
USEFUL FOR

Students studying trigonometry, educators teaching sinusoidal functions, and anyone interested in graphing techniques for periodic functions.

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Phase shift and sinusoidal curve fitting - Finding...

Homework Statement



"Find the period, amplitude, and phase shift of each function. Graph each function. Be sure to label key points"

y = 4sin(2x - pi)


Homework Equations





The Attempt at a Solution



So, I got...

Amplitude = 4
Period = 2pi/2 = 2

Phase shift: Would that be pheta/w ?, So pi/2 ?

Now here is where I get messed up.

I do not know how to get "Interval defining one cycle" and "Subinterval width"

How do I generate points from this?
 
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First step: Graph paper. Sharp pencil. Eraser. Calculator. Plot points in steps of, say 0.1 radian, for x from 0 to 2Pi radians, plotting y vs. x

Then, complete the plot from 0 back to -Pi radians.

Do this neatly & well, and you'll discover a lot.
 
Last edited:

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