Solving Closest Values of x to Zero: Formula to Make it Easy

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Discussion Overview

The discussion revolves around solving the equation -30 sin 3x = 1/10 cos 3x to find the two values of x that are closest to zero. Participants explore methods and formulas that could simplify this process.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant expresses difficulty in solving the equation for x and inquires about a simplifying formula.
  • Another participant suggests rewriting the equation in terms of tan(3x) as a potential approach.
  • A third participant provides a brief explanation of the relationship between sine, cosine, and tangent, referencing a right triangle to illustrate the concept.
  • A later reply acknowledges the previous contributions with a note of appreciation.

Areas of Agreement / Disagreement

Participants have not reached a consensus on a specific method to solve the equation, and the discussion includes varying approaches and suggestions.

Contextual Notes

The discussion does not clarify the assumptions or steps needed to transition from the original equation to the suggested tangent form, leaving some mathematical details unresolved.

john425
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I am having trouble solving for the two values
of (x) that are closest to zero.

-30 sin 3x = 1/10 cos 3x

Is there a formula I could use to make this easy?
 
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Write this as an equation in tan(3x)..
 
sin(x)/cos(x) = tan(x)

to see why this is true Draw a right triangle with hypotenuse 1 and an acute angle x, you can work the sides of the right triangle have lengths sin(x) and cos(x).
 
Oh yea! I just forgot!

Thank you!
 

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