Still celebrating National IT Professionals Day with 3 months of free Premium Membership. Use Code ITDAY17

x
?
Solved

Solution of an equation

Posted on 2013-11-24
9
Medium Priority
?
327 Views
Last Modified: 2013-12-13
Can someone solve this equation? A colleague gave this. This is not homework

Equation
0
Comment
Question by:Saqib Husain, Syed
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 5
  • 3
9 Comments
 
LVL 84

Expert Comment

by:ozo
ID: 39673365
φ=n*2pi, where n ∈ Z
0
 
LVL 43

Author Comment

by:Saqib Husain, Syed
ID: 39679855
Is there a way to reduce the terms and get an expression for phi?
0
 
LVL 84

Expert Comment

by:ozo
ID: 39679879
Yes.  see above.
0
Concerto's Cloud Advisory Services

Want to avoid the missteps to gaining all the benefits of the cloud? Learn more about the different assessment options from our Cloud Advisory team.

 
LVL 84

Expert Comment

by:ozo
ID: 39679893
phi = n*2pi, where n is an integer.
0
 
LVL 43

Author Comment

by:Saqib Husain, Syed
ID: 39679917
Ok, but can I have some algebraic steps which can lead me to that result?


φ=n*2pi, where n ∈ Z
I do not understand the & and ; symbols neither do I understand the Z
0
 
LVL 84

Expert Comment

by:ozo
ID: 39679928
http:#a39679893 repeats the solution without the symbols.

For the algebra, let x = sin(phi), rewrite the trig functions in terms of sin, and solve for x, than take arcsin(x)
0
 
LVL 27

Expert Comment

by:BigRat
ID: 39680756
ozo's solution is a trivial solution because the sine of any multiple of 2*pi  is zero, the cosine is 1, and the tangent of half the angle (180) also is zero. So the entire RHS reduces to 1. Thus any integer multiple of 2pi is a solution.

If you multiply out the denominator you'll get the left hand term as a power of the constant e equal to a right hand term which does not involve e in the same degree, that is the tangent expression of phi over 2 does not contain an e term. This means that phi must be given in terms of e and therefore in non-trigometrical terms as well.

I suspect thate there is no simple algebraic solution.
0
 
LVL 84

Accepted Solution

by:
ozo earned 2000 total points
ID: 39682622
I dropped a parenthesis in my derivation, and missed a cos(phi) cancellation, which caused me to omit the odd pi solutions;
phi = n*p where n is an integer

You can reduce all the trig to
(1+s)*(1-es)^e - (1+es)^(e+1) = 0  [for s!=1]
where s=sin(phi)
0
 
LVL 43

Author Closing Comment

by:Saqib Husain, Syed
ID: 39716014
Sorry did not get the chance to try this but it is time to close this now. Thanks for the effort.
0

Featured Post

What does it mean to be "Always On"?

Is your cloud always on? With an Always On cloud you won't have to worry about downtime for maintenance or software application code updates, ensuring that your bottom line isn't affected.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

How to Win a Jar of Candy Corn: A Scientific Approach! I love mathematics. If you love mathematics also, you may enjoy this tip on how to use math to win your own jar of candy corn and to impress your friends. As I said, I love math, but I gu…
We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…
Suggested Courses

715 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question