amsterdam11
Could someone please help me with sqrt(3) tan2x=0
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lgbasallote
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what do you want to do with it?
amsterdam11
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solve for x
lgbasallote
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\[\sqrt 3 \tan (2x) = 0\]
first step divide both sides by \(\sqrt{3}\) what do you get?
y2o2
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x = 0 or x = 180
amsterdam11
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so tan2x=-1/sqrt(3)
lgbasallote
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nope. \[\tan (2x) =\frac {0}{\sqrt3}\]
now simplify this
amsterdam11
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oh dear! sorry i didnt realise! The question is sqrt(3) tan2x+1=0
amsterdam11
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sorry!
lgbasallote
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haha..then you're right \[\tan(2x) =-\frac{1}{\sqrt 3}\]
lgbasallote
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now second step. take the arctangent of both sides
amsterdam11
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ok so pi/6?
lgbasallote
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remember that negative sign...and it's not yet over
amsterdam11
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how does the negative affect it?
lgbasallote
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well it doesnt affect that much
amsterdam11
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how do you mean?
lgbasallote
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|dw:1342705038280:dw|
amsterdam11
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oh ok so when you say take the arctangent, where do you go from there?
lgbasallote
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so \[2x = -\frac{\pi}{6}\]
now you divide both sides by 2
amsterdam11
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ok so x= =pi/12
amsterdam11
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-pi/12
lgbasallote
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yup
amsterdam11
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is this one of the answers?
lgbasallote
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what do you mean?
amsterdam11
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well there are 4 values for x right?
amsterdam11
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because there was a 2 between the tan and the x, which compresses the tan graph
lgbasallote
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i cant remember that part...is it adding \(\pi\) or \(2\pi\)
lgbasallote
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what do you mean 2 between tan and x..tan (2x)?
amsterdam11
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yeah, thats what i meant tan2x
amsterdam11
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i think its add pi
lgbasallote
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im not sure about this part so im gonna ask @amistre64 for some assistance. please come sir.
amsterdam11
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Thank you for your help so far!!
amsterdam11
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what does amistre64 say?
lgbasallote
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i dont think he's coming yet...i tried tagging him to come here...
lgbasallote
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let me call a different one..he might be afk
amsterdam11
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Thank you :)
lgbasallote
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@apoorvk pls help
vamgadu
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just add pi to the solution and it wont matter.
amsterdam11
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so 11pi/12?
vamgadu
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yep i do think its another answer.
lgbasallote
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thanks @vamgadu you saved me there heh
amsterdam11
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yes thank you! :)
vamgadu
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its my pleasure @lgbasallote
amsterdam11
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however, in the back of my text book the answers are 5pi/12 11pi/12 17pi/12 and 23pi/12
amsterdam11
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and im wondering how my magic maths textbook got there
amsterdam11
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so we are going good with the 11pi/12 :D
amsterdam11
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and if pi is added again, we get 23pi/12 which is also good!
lgbasallote
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you're doing right. so is there a further problem?
amsterdam11
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well there are sposed to be 4 answers
lgbasallote
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then you add pi again
amsterdam11
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i have 2 :)
lgbasallote
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2?
vamgadu
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subtract a pi, if want int he interval, [-2pi,2pi]
amsterdam11
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well i have 11pi/12 and 23pi/12
vamgadu
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-pi/12 and -13pi/12
amsterdam11
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so 11pi/12-pi?
lgbasallote
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-pi/12 - pi
lgbasallote
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11pi/12 - pi is -pi/12 (bringing you back to the orig thingy)
amsterdam11
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thats not one of the answers :?
phi
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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] )
amsterdam11
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can this be done on a tan graph?