How Do Symmetric Graphs Relate to Equations and Calculations?

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SUMMARY

This discussion focuses on the relationship between symmetric graphs and their corresponding equations, specifically addressing the multiplication of factors such as (x-2)(x+2) and the implications of symmetry about the origin. Participants emphasize the importance of visualizing solutions through plotting, particularly for equations like x = 0.5 cos x. Additionally, the application of trigonometric principles, including the tangent function and the law of sines, is highlighted in solving related problems.

PREREQUISITES
  • Understanding of polynomial factorization, specifically (x-2)(x+2).
  • Familiarity with trigonometric functions, including tangent and cosine.
  • Basic graphing skills to visualize equations and their solutions.
  • Knowledge of the law of sines for solving triangles.
NEXT STEPS
  • Learn how to plot equations using graphing software or tools like Desmos.
  • Study the properties of symmetric functions and their graphical representations.
  • Explore the method for solving equations involving trigonometric identities, particularly x = 0.5 cos x.
  • Review the law of sines and its applications in solving triangle-related problems.
USEFUL FOR

Students in mathematics, educators teaching algebra and trigonometry, and anyone interested in understanding the graphical representation of equations and their symmetries.

whitehorsey
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1. See Attachments



2. None



3. 1st Attachment #19 I believe that I am suppose to multiply (x-2)(x+2) but what do i do about the symmetric with an origin?

2nd Attachment I do not get what they are asking for in the 2nd and 3rd part of the question can you please explain it to me.

3rd Attachment I am not sure if I did this problem right.
tan 1.2 = h/10
h = 25.72 km?

Thank You!
 

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whitehorsey said:
1. See Attachments



2. None



3. 1st Attachment #19 I believe that I am suppose to multiply (x-2)(x+2) but what do i do about the symmetric with an origin?
Did you plot your solution?
2nd Attachment I do not get what they are asking for in the 2nd and 3rd part of the question can you please explain it to me.

You need to find the x which satisfies x = .5 cos x.
They give pretty explict directions on how to start. Did you make the plot they ask for? if not do so.
3rd Attachment I am not sure if I did this problem right.
tan 1.2 = h/10
h = 25.72 km?

Thank You![/b]

Draw a picture, This may be a good place for the law of sines.
 

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