Could someone please help me with sqrt(3) tan2x=0

- anonymous

Could someone please help me with sqrt(3) tan2x=0

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- lgbasallote

what do you want to do with it?

- anonymous

solve for x

- lgbasallote

\[\sqrt 3 \tan (2x) = 0\]
first step divide both sides by \(\sqrt{3}\) what do you get?

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## More answers

- y2o2

x = 0 or x = 180

- anonymous

so tan2x=-1/sqrt(3)

- lgbasallote

nope. \[\tan (2x) =\frac {0}{\sqrt3}\]
now simplify this

- anonymous

oh dear! sorry i didnt realise! The question is sqrt(3) tan2x+1=0

- anonymous

sorry!

- lgbasallote

haha..then you're right \[\tan(2x) =-\frac{1}{\sqrt 3}\]

- lgbasallote

now second step. take the arctangent of both sides

- anonymous

ok so pi/6?

- lgbasallote

remember that negative sign...and it's not yet over

- anonymous

how does the negative affect it?

- lgbasallote

well it doesnt affect that much

- anonymous

how do you mean?

- lgbasallote

|dw:1342705038280:dw|

- anonymous

oh ok so when you say take the arctangent, where do you go from there?

- lgbasallote

so \[2x = -\frac{\pi}{6}\]
now you divide both sides by 2

- anonymous

ok so x= =pi/12

- anonymous

-pi/12

- lgbasallote

yup

- anonymous

is this one of the answers?

- lgbasallote

what do you mean?

- anonymous

well there are 4 values for x right?

- anonymous

because there was a 2 between the tan and the x, which compresses the tan graph

- lgbasallote

i cant remember that part...is it adding \(\pi\) or \(2\pi\)

- lgbasallote

what do you mean 2 between tan and x..tan (2x)?

- anonymous

yeah, thats what i meant tan2x

- anonymous

i think its add pi

- lgbasallote

im not sure about this part so im gonna ask @amistre64 for some assistance. please come sir.

- anonymous

Thank you for your help so far!!

- anonymous

what does amistre64 say?

- lgbasallote

i dont think he's coming yet...i tried tagging him to come here...

- lgbasallote

let me call a different one..he might be afk

- anonymous

Thank you :)

- lgbasallote

@apoorvk pls help

- anonymous

just add pi to the solution and it wont matter.

- anonymous

so 11pi/12?

- anonymous

yep i do think its another answer.

- lgbasallote

thanks @vamgadu you saved me there heh

- anonymous

yes thank you! :)

- anonymous

its my pleasure @lgbasallote

- anonymous

however, in the back of my text book the answers are 5pi/12 11pi/12 17pi/12 and 23pi/12

- anonymous

and im wondering how my magic maths textbook got there

- anonymous

so we are going good with the 11pi/12 :D

- anonymous

and if pi is added again, we get 23pi/12 which is also good!

- lgbasallote

you're doing right. so is there a further problem?

- anonymous

well there are sposed to be 4 answers

- lgbasallote

then you add pi again

- anonymous

i have 2 :)

- lgbasallote

2?

- anonymous

subtract a pi, if want int he interval, [-2pi,2pi]

- anonymous

well i have 11pi/12 and 23pi/12

- anonymous

-pi/12 and -13pi/12

- anonymous

so 11pi/12-pi?

- lgbasallote

-pi/12 - pi

- lgbasallote

11pi/12 - pi is -pi/12 (bringing you back to the orig thingy)

- anonymous

thats not one of the answers :?

- phi

You started with
2x= -pi/6
if we call 2x theta, we have 2 solutions:
|dw:1342706814544:dw|
and x is 5pi/12 and 11pi/12
now add pi to each value to get the other 2 solutions
or , noting that 2x+pi divided by 2 is x+pi/2 , add multiplies of pi/2 to get all four solutions starting with -pi/12 (which is 11pi/12 in the interval [0, 2pi] )

- anonymous

can this be done on a tan graph?

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