stephaniejsa123 stephaniejsa123
  • 18-03-2019
  • Mathematics
contestada

How do I solve cos x> 1/2 sin x?

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LammettHash
LammettHash LammettHash
  • 18-03-2019

Divide both sides by [tex]\dfrac12\cos x[/tex]:

[tex]\dfrac{\cos x}{\frac12\cos x}>\dfrac{\frac12\sin x}{\frac12\cos x}\implies2>\dfrac{\sin x}{\cos x}=\tan x[/tex]

If [tex]-\dfrac\pi2<x<\dfrac\pi2[/tex], then

[tex]\tan x<2\implies-\dfrac\pi2<x<\tan^{-1}2[/tex]

and more generally, for any integer [tex]n[/tex],

[tex]n\pi-\dfrac\pi2<x<n\pi+\tan^{-1}2[/tex]

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