Trigonometry Circular and Inequalities: Homework Statement and Solution Attempt

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SUMMARY

The discussion focuses on solving a trigonometric inequality involving the tangent function, specifically the inequality \(\sqrt{3}\tan(3x+\frac{\pi}{3})<3\). The user attempts to solve this by determining the range of \(x\) that satisfies the inequality, concluding that \(0>\frac{-5\pi}{18}\). A key question arises regarding the difference in results when substituting \(\frac{3\pi}{2}\) for \(-\frac{\pi}{2}\) in the solution process.

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  • Knowledge of solving inequalities involving trigonometric expressions.
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  • Basic algebra skills for manipulating inequalities.
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  • Review the unit circle to better understand angle transformations.
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Homework Statement



I have one trigonometry circular, like on this "[PLAIN 00211.jpg"]picture.[/URL]

On the picture there are pi/2 and -pi/2.

Also I have another picture with inequality which "[PLAIN 00211.jpg"]I need to solve.[/URL]

Homework Equations


The Attempt at a Solution



\sqrt{3}tg(3x+\frac{\pi}{3})&lt;3

tg(3x+\frac{pi}{3})&lt;\sqrt{3}I have another "[URL 0021111.JPG"]picture.[/URL]

So the results for tg are:

\frac{\pi}{3}&gt;3x+\frac{pi}{3}&gt;\frac{-\pi}{2}

so the results for x are

0&gt;\frac{-5\pi}{18}

The question is: will I get same if I use \frac{3\pi}{2} instead of \frac{\-pi}{2}
 
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Hi Physicsissuef! :smile:

more information needed …

what is x? is it an angle (if it isn't, how can you add it to π/2?)

what are the two horizontal lines supposed to be?

what are you being asked to solve? :confused:
 
x is angle. I asked why I don't get same when I use \frac{3\pi}{2} instead of \frac{-\pi}{2}?
 

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