Solution of equation

  • Thread starter Nyasha
  • Start date
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1. The problem statement, all variables and given/known data

Find all solutions to the following equation: [tex]3tan(Inx)=2[/tex]



3. The attempt at a solution

[tex]tan(Inx)=2/3[/tex]

[tex]Inx=arctan(2/3)[/tex]

x=e^(arctan(2/3)
 
Last edited:

lanedance

Homework Helper
3,305
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Hi Nyasha
i think you mean ln(x) = arctan(2/3)?
 

lanedance

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note the potential for multiple solutions
 
127
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Hi Nyasha
i think you mean ln(x) = arctan(2/3)?

Yes thats what l meant and my answer is x=e^(arctan(2/3). How do you get multiple solutions ?
 

lanedance

Homework Helper
3,305
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think about a graph of the function
y = tanx
it basically repeats along the axis every 2.pi

when you take the arctan, you can think of it as picking a y value, tracing it out to across to where it intersects the curve, and dropping down to the x value, giving you
x = arctan(y)

how do you choose a curve to use....? multiple solutions... how many are there?
 
127
0
think about a graph of the function
y = tanx
it basically repeats along the axis every 2.pi

when you take the arctan, you can think of it as picking a y value, tracing it out to across to where it intersects the curve, and dropping down to the x value, giving you
x = arctan(y)

how do you choose a curve to use....? multiple solutions... how many are there?
Are you trying to say it has multiple solutions because the domain of arctan is from -∞ to ∞
 

lanedance

Homework Helper
3,305
2
no, to make it single valued, you must confine the range

think of your diagram of y = tanx
a vertical line will one graph
A horizontal will intersect many

try drawing y = arctanx
what does it look like? will essentially be your prvious graph rotated by 90degreees
 

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