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-1<=sqrt(3)tgx<=1

Guest Jun 13, 2017
 #1
avatar+7266 
+2

\(\begin{array} \ -1\leq\sqrt3\tan x \leq1 \\~\\ -1\leq\sqrt3\tan x&\qquad&\sqrt3\tan x \leq 1 \\~\\ -\frac{1}{\sqrt3}\leq\tan x &\qquad& \tan x \leq \frac{1}{\sqrt3} \\~\\ -\frac{\sqrt3}{3}\leq\tan x &\qquad& \tan x \leq \frac{\sqrt3}{3} \\~\\ \arctan(-\frac{\sqrt3}{3}) \leq x &\qquad& x \leq \arctan(\frac{\sqrt3}{3}) \\~\\ -30^{\circ}+180^{\circ}n \leq x &\qquad& x \leq 30^{\circ}+180^{\circ}n \qquad\text{, where n is an integer}\\~\\ -30^{\circ}\leq x-180^{\circ}n &\qquad&30^{\circ}\leq x-180^{\circ}n \\~\\ -30^{\circ}\leq x-180^{\circ}n\leq30^{\circ}\end{array}\)

 

 

So...for instance...

-30º   ≤  x  ≤  30º

150º  ≤  x  ≤  210º

330º  ≤  x  ≤  390º

 

I think this is right, but I am not 100% confident in this answer...

hectictar  Jun 13, 2017
edited by Guest  Jun 13, 2017
 #2
avatar+26971 
+1

This graph should help you to be confident!

 

.

Alan  Jun 14, 2017

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