x = cosx/sinx FIND X HELP

[dtsy]

[h=2]x = cos(x)/sin(x) FIND X[/h]

thank you in advance xx

 

[Deleted member 4993]

x = cos(x)/sin(x) FIND X



thank you in advance xx

There is no closed form solution to this problem. What have you been taught regarding solution of non-linear equations?

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[dtsy]

There is no closed form solution to this problem. What have you been taught regarding solution of non-linear equations?

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

Thanks for answering x
I am trying to find the stationary points of the graph f(x)=xcos(x) with domain [-pi, pi]
so i figured f'(x)=cos(x)-xsin(x)
stationary points are when f'(x)=0
so cos(x)=xsin(x)

 

[Deleted member 4993]

Thanks for answering x
I am trying to find the stationary points of the graph f(x)=xcos(x)
so i figured f'(x)=cos(x)-xsin(x)
stationary points are when f'(x)=0
so cos(x)=xsin(x)

Plot the function from x = -5 to +5 and estimate the stationary points (if you do not know the numerical method to estimate the values).

 

[Deleted member 4993]

Plot the function from x = -5 to +5 and estimate the stationary points (if you do not know the numerical method to estimate the values).

There are infinite numbers of stationary points for y = x * sin(x) - like you have in sin(x) and/or cos(x) or any other cyclical functions.

 

[Ishuda]

Thanks for answering x
I am trying to find the stationary points of the graph f(x)=xcos(x) with domain [-pi, pi]
so i figured f'(x)=cos(x)-xsin(x)
stationary points are when f'(x)=0
so cos(x)=xsin(x)

f'(x)=0 does give the equation
x = cos(x)/sin(x) = cot(x)
Now, since cot(x) is an odd function if we have a positive x which satisfies the equation, so will the negative of that. That is, assume
x₀ = cot(x₀)
then
-x₀ = cot(-x₀) = - cot(x₀).
Also if a negative x is a solution, so the positive value. So we only need to look at positive x.

If you plot the two functions y=x and y=cot(x) for x positive between zero and $\displaystyle \pi$ you will see that they cross between x=0.8 and 0.9. To get closer use Newtons method or some other numerical method for finding the value. One you find the value, don't forget the negative of that is also a solution.

 

[Bob Brown MSEE]

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