How do I solve goniometric inequations with cosine and tangent?

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Homework Help Overview

The discussion revolves around solving goniometric inequations involving cosine and tangent functions, specifically cos(7x) > cos(3x) and tan(x) > -3.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to determine the range of x for the inequation tan(x) > -3, questioning the upper limit of x. Participants suggest various interpretations of the solution, including the use of arctan and periodicity.

Discussion Status

Participants are exploring different interpretations of the inequations, with some suggesting possible ranges for x while others question the validity of including multiple values for k in the solutions. There is an ongoing dialogue about the implications of these interpretations.

Contextual Notes

There is a noted confusion regarding the application of periodicity in the context of the inequations, as well as the handling of multiple solutions represented by k.

scientifico
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Hello, how can I solve cos(7x) > cos(3x) and tan(x) > -3 ?

I know in the second one x is greater than -arctan(3) but smaller than what?

Thanks!
 
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hi scientifico! :smile:

arctan(∞) ? :wink:
 
90° + k*180°
 
yes :smile:

(and of course you'll need the same " + k*180° " for arctan(-3) )
 
x < -arctan(3) + k*180° ?
 
that makes no sense :redface:

you can't have one equation (or inequation) with a multiple-value k !
 
270°+ k*180° < x < -arctan(3) + k*180°
 

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