SOLUTION: I need to solve this equation for 0 < x< 2pi -2tan(-2x + 4pi/3) = 2sqrt3

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Question 1063200: I need to solve this equation for 0 < x< 2pi
-2tan(-2x + 4pi/3) = 2sqrt3
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
I need to solve this equation for 0 < x< 2pi
-2tan(-2x + 4pi/3) = 2sqrt3
-----
tan(-2x+(4/3)pi) = -sqrt(3)
----
Take the arctan of both sides to get:
-2x+(4/3)pi = (2/3)pi or (5/3)pi
-----
-2x = (-2/3)pi or (1/3)pi
------
x = (1/3)pi or (-2/3)pi
------------------------
Cheers,
Stan H.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
I need to solve this equation for 0 < x < 2pi
-2tan(-2x + 4pi/3) = 2sqrt3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

 =   ----->  (divide both sides by (-2) )  --->

 =   ---->  

The last equation has solutions   = , k = 0, +/-1, +/-2, , , , .


Let's derive an expression for x from this:
 

 =    ---->   =   ---->   =   ---->  x = , k = 0, +/-1, +/-2, , , , .

In the given interval (,) 

x = , , ,  are the solutions.

Answer. In the given interval the solutions are   = , , , .    (See the plot below)



Plots y = and y =

To see more examples of solved trigonometry equations with detailed solutions, look into the lessons
    - Solving simple problems on trigonometric equations
    - Solving typical problems on trigonometric equations
    - Solving more complicated problems on trigonometric equations
    - Solving advanced problems on trigonometric equations
    - Proving Trigonometry identities
    - OVERVIEW of lessons on calculating trig functions and solving trig equations
in this site.


Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Trigonometry: Solved problems".



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