another trig question (1 Viewer)

alez

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can i just say, i totally loathe the fitzpatrick book
anyway
3tan2x=2tanx
i changed the tan2x into 2tanx/1-tan^2 x
then divided both sides by 2tanx
but kinda ended up with tan^2 x=-2
help
 
P

pLuvia

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You can't just divide by 2tanx, that would mean you are eliminating one of the solutions.

Better way would be to factorise it then you'll get your answer

The answer is 0, pi, 2pi, 3pi. Depending on the domain of the function, the answers could go on forever
 
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conics2008

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Hi there, I speak English.

3tan(2x)=2tan(x) >> Use The double angel shit tan(2x) = 2tan(x)/1-tan^2(x)

3(2tan(x)/1-tan^2(x)) = 2tan(x) >> take away the base

6tan(x)=2tan(x)-2tan^3(x) >> collect like terms

4tan(x)+2tan^3(x)=0 >> now you can see x = 0 is a root.

but when you factorise the get shit out of it, you get something like tan^2(x)=-2

now you cant square root a negative number right ? so you ignore it since its not REAL ( wow I feel soo big saying this word REAL )

ok so you know tan(x)=0 >>> the thing with trig is that it can have alot of roots

now look for values that make tan(x) =0

in the 1st quadrant and in the 3rd right ? 3rd Quad uses 180+Theta

therefore roots are

0,180 for the first revolution
then 360,540 2nd revolution and so on..


how I got 360 I do this, see the first 2 rounds you got 0 and 180 soo when you start another revoultion you do

360+0 , 360 + 180 and so on...

GOOD LUCKKKKKKKKK .. I speak english
 

lolokay

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yeah dividing by 2tanx is dividing by zero in this case
 

~Fire Jade~

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I hope this doesn't confuse you even more than you already are...
I think this is how you do it....

3tan2x=tanx
Use the double angle formula crap:bomb:
3[(2tanx)/(1-tan^2x)]=tanx
Move the bottom thingo on the LHS to the RHS...and u end up with something like this...
6tanx=tanx (1-tan^2x)
u expand it
6tanx=tanx- tan^3x
0=tan^3x+ 5tanx
Factorise it
0=tanx(tan^2x+5)
Solun:
tanx=0 or tan^2x=-5 (no solun??)
Solve it from there
:burn:
I don't know whether this is right and I take no responsibility for this junk if its wrong. lols.:rofl:
 

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