How do you solve $3 tan x - \sqrt{3} = 0$ $3tanx-sqrt3=0$ and find all solutions in the interval $[0, 2 π)$ $[0,2pi)$ ?

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How do you solve $3 tan x - \sqrt{3} = 0$ $3tanx-sqrt3=0$ and find all solutions in the interval $[0, 2 π)$ $[0,2pi)$ ?

1 Answer

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Answer 1 · 2016-07-12T15:35:21

$(\frac{π}{6}$ $(pi/6$ , $\frac{7 \cdot π}{6})$ $(7*pi)/6)$

Explanation:

$3 \cdot tan x - \sqrt{3} = 0$ $3*tan x-sqrt3=0$
$3 \cdot tan x = \sqrt{3}$ $3*tan x =sqrt3$
$tan x = \frac{\sqrt{3}}{3}$ $tan x =sqrt3/3$
$arctan (\frac{\sqrt{3}}{3}) = \frac{π}{6}$ $arctan(sqrt3/3)=pi/6$
The tan function has a period of $π$ $pi$ , so it will repeat at $π + \frac{π}{6}$ $pi+pi/6$ or $\frac{7 \cdot π}{6}$ $(7*pi)/6$

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How do you solve $3 tan x - \sqrt{3} = 0$ $3tanx-sqrt3=0$ and find all solutions in the interval $[0, 2 π)$ $[0,2pi)$ ?

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How do you solve $3 tan x - \sqrt{3} = 0$ $3tanx-sqrt3=0$ and find all solutions in the interval $[0, 2 π)$ $[0,2pi)$ ?