anonymous
  • anonymous
Solve: (tan x - 1)(tan x - √3) = 0 0≤Ɵ<2π
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
tanx-1=0 tanx-sqrt(3)=0 tanx=1 tanx=sqrt(3) for tanx=1, x=pi/4 tangent is also positive in the 3rd quadrant, so subtract pi/4 from 3pi/2 to get your second answer for this half of the equation. follow the same rules for tanx=sqrt(3)
anonymous
  • anonymous
Where is the 3pi/2 come from ?
anonymous
  • anonymous
3pi/2-pi/4 will give you a solution in the 3rd quadrant

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anonymous
  • anonymous
where tangent is also positive
anonymous
  • anonymous
its the same as pi/4+pi
anonymous
  • anonymous
pi/4+pi=3pi/2-pi/4=5pi/4
anonymous
  • anonymous
Sorry if it's a silly questions but how is pi/4 + pi = 3pi/2 ? can you please explain this part, cuz I'm really confuse in class too about all this pi thing
anonymous
  • anonymous
\[\frac{\pi}{4}+\pi=\frac{\pi}{4}+\frac{4\pi}{4}=\frac{\pi+4\pi}{4}=\frac{5\pi}{4}\]
anonymous
  • anonymous
pi/4+pi does not equal 3pi/2 it equals 3pi/2-pi/4
anonymous
  • anonymous
both pi/4+pi and 3pi/2-pi/4 equal 5pi/4
anonymous
  • anonymous
see how i multiplied pi above by 4/4, this is to get each term with an LCD
anonymous
  • anonymous
then the addition is simple
anonymous
  • anonymous
i've only given you 2 solutions so far. pi/4 and 5pi/4. there are 2 more solutions resulting from: tanx=sqrt(3)
anonymous
  • anonymous
oh ok
anonymous
  • anonymous
i got one it's pi/3
anonymous
  • anonymous
yes, and the 2nd one is?
anonymous
  • anonymous
add pi to pi/3
anonymous
  • anonymous
4pi/3
anonymous
  • anonymous
right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Thanks you so much Dockworker ! :D
anonymous
  • anonymous
those are all solutions in the domain 0<=x<=2pi
anonymous
  • anonymous
Ok
anonymous
  • anonymous
yw

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