# how to solve these equations

Discussion in 'C++' started by vj, Aug 23, 2006.

1. ### vjGuest

Hi all,

I want to solve the two equations

u*tan(u)=w
and
u^2 + w^2=V^2, where V is a known constant, and u and w are the two
unknowns to be determined. Please can someone suggest me how to write a
code and solve these equations in C or C++? I am not an expert, but
have elementary working knowledge of C.

Thanks

vj

vj, Aug 23, 2006

2. ### Noah RobertsGuest

vj wrote:
> Hi all,
>
> I want to solve the two equations
>
> u*tan(u)=w
> and
> u^2 + w^2=V^2, where V is a known constant, and u and w are the two
> unknowns to be determined. Please can someone suggest me how to write a
> code and solve these equations in C or C++? I am not an expert, but
> have elementary working knowledge of C.

You need algebra.

If these are a system then it can easily be solved using math.

If they are not a system the only way to "solve" such equations is to
loop until you get to a certain point close to the answer. It doesn't
look to me like that kind of problem though. Some equations are not
solvable but you know when you get close to your answer and how to
change the variable to get closer. I find this a lot in my job working
on software that makes use of fluid mechanics in calculations.

You can also solve them for input in one of the variables and output
the value of the other. This is also a simple matter of using basic
algebra to solve for a variable.

Noah Roberts, Aug 23, 2006

3. ### Victor BazarovGuest

vj wrote:
> I want to solve the two equations
>
> u*tan(u)=w
> and
> u^2 + w^2=V^2, where V is a known constant, and u and w are the two
> unknowns to be determined. Please can someone suggest me how to write
> a code and solve these equations in C or C++? I am not an expert, but
> have elementary working knowledge of C.

You need to look up "Newton-Raphson method", most likely. It's not
topical here. Try sci.math.* hierarchy.

Since you have elementary working knowledge of C, you already know how
"to write a code". Begin with "int main(" and proceed to write all
the necessary code for the algorithm that you already have. If you
don't have the algorithm, we can't help you. It's not a C++ language
problem.

V
--

Victor Bazarov, Aug 23, 2006
4. ### Douglas ReedGuest

vj,

The first hit on google, if you search for "solving systems of
equations" (no quotes).

http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=syslin

Doug

vj wrote:
> Hi all,
>
> I want to solve the two equations
>
> u*tan(u)=w
> and
> u^2 + w^2=V^2, where V is a known constant, and u and w are the two
> unknowns to be determined. Please can someone suggest me how to write a
> code and solve these equations in C or C++? I am not an expert, but
> have elementary working knowledge of C.
>
> Thanks
>
> vj
>

Douglas Reed, Aug 23, 2006
5. ### Ural MutluGuest

On Wed, 23 Aug 2006 08:34:37 -0700, vj wrote:

> Hi all,
>
> I want to solve the two equations
>
> u*tan(u)=w
> and
> u^2 + w^2=V^2, where V is a known constant, and u and w are the two

this looks like a trigonometrical problem. assume there is a triangle with
the right angle sides u ans w and the opposite side V, eg, pythagorian
triangle..

the first equation is tan(u)=w/u which is the normal definition of tan()
but the angle in numbers must be equal to one of the sides. I presume the
u in tan(u) is in radians not in degrees?

thats all i can see for now..

> unknowns to be determined. Please can someone suggest me how to write a
> code and solve these equations in C or C++? I am not an expert, but have
> elementary working knowledge of C.
>
> Thanks
>
> vj

Ural Mutlu, Aug 23, 2006
6. ### Ural MutluGuest

> You need algebra.
>
> If these are a system then it can easily be solved using math.
>
> If they are not a system the only way to "solve" such equations is to
> loop until you get to a certain point close to the answer. It doesn't
> look to me like that kind of problem though. Some equations are not
> solvable but you know when you get close to your answer and how to
> change the variable to get closer. I find this a lot in my job working
> on software that makes use of fluid mechanics in calculations.
>
> You can also solve them for input in one of the variables and output
> the value of the other. This is also a simple matter of using basic
> algebra to solve for a variable.

my instinct tells me the solution to this problem is to loop until you get
close to an answer. basically a brute force solution

Ural Mutlu, Aug 23, 2006
7. ### Mark PGuest

vj wrote:
> Hi all,
>
> I want to solve the two equations
>
> u*tan(u)=w
> and
> u^2 + w^2=V^2, where V is a known constant, and u and w are the two
> unknowns to be determined. Please can someone suggest me how to write a
> code and solve these equations in C or C++? I am not an expert, but
> have elementary working knowledge of C.
>
> Thanks
>
> vj
>

Replace w in the second equation with its expression in terms of u. Use
the trig identity 1 + tan^2 = sec^2 and apply a square root to make it
even simpler. Then look up Newton's method.

Mark P, Aug 23, 2006
8. ### r normanGuest

On Wed, 23 Aug 2006 17:04:10 GMT, Mark P
<> wrote:

>vj wrote:
>> Hi all,
>>
>> I want to solve the two equations
>>
>> u*tan(u)=w
>> and
>> u^2 + w^2=V^2, where V is a known constant, and u and w are the two
>> unknowns to be determined. Please can someone suggest me how to write a
>> code and solve these equations in C or C++? I am not an expert, but
>> have elementary working knowledge of C.
>>
>> Thanks
>>
>> vj
>>

>
>Replace w in the second equation with its expression in terms of u. Use
>the trig identity 1 + tan^2 = sec^2 and apply a square root to make it
>even simpler. Then look up Newton's method.

This query has all the earmarks of a homework problem, in my opinion.
Some help and guidance, like "look up Newton's method" might be
appropriate. I am not sure just how much more explicit information
would be.

r norman, Aug 23, 2006
9. ### Default UserGuest

Douglas Reed wrote:

> vj,

with properly trimmed quotes. See the majority of other posts in the
newsgroup, or the group FAQ list:
<http://www.parashift.com/c++-faq-lite/how-to-post.html>

Brian (lots of 'em today)

Default User, Aug 23, 2006

Joined:
Sep 23, 2011
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