given value of y, find value of x in tan (x) - x = y

A

AndrewR88

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Feb 4, 2007
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I'm having trouble figuring out how to find the x value if given the y.

tan (x) - x = y

0 < x < pi/2
 
You should have trouble with that. It is not a trivial task.

You can use graphic techniques to get close.

For y = 0, graph g(x) = tan(x) and f(x) = x and see if you can observe an intersection.

For y = 1, graph g(x) = tan(x) and f(x) = 1+x and see if you can observe an intersection.

Since you are in Calculus, have you met "Newton's Method", or "Bisection", or various other numerical techniques?
 
Yes we have gone over newton's method but the problem is it has to be able to be converted correctly in excel..
any ideas on that?
 
tanx - x =y
given y find x
Newtons - Raphson , usually called Newtons method

f[x]= tanx -[x+y] y a parameter
f' [x]= 1/cos^2x -1

x1 =x0 - f[x0] / f'[x0]

I do not know what excel is, but this reitterive process can be carried out to as many decimal places as needed.

Arthur
 
AndrewR88 said:
Yes we have gone over newton's method but the problem is it has to be able to be converted correctly in excel..
any ideas on that?
Click to expand...
Sure! How are you at defining your own functions? There's plenty that can be done in VBasic.

Short of that, you can just simplfy the expression as much as possible and code it. Make it use values above the formula (relative references) and just copy it down.
 
ah i did not know you could make your own function! Now my only problem is that if I use newton's method, it will always only give me the zero of the function.. Or maybe im just not using it right?
 
If you start with f(x) = 0, you will, indeed, get a zero - if it converges.

If you want f(x) = 3, for example, simply modify it. [f(x) - 3] = 0 and do it anyway with a slightly different function.
 
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