Go Premium for a chance to win a PS4. Enter to Win

x
?
Solved

Solution of an equation

Posted on 2013-11-24
9
Medium Priority
?
338 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
  • 5
  • 3
9 Comments
 
LVL 85

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 85

Expert Comment

by:ozo
ID: 39679879
Yes.  see above.
0
Industry Leaders: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

 
LVL 85

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 85

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 85

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

Industry Leaders: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

Question has a verified solution.

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

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.
Aerodynamic noise is the cause of the majority of the noise produced by helicopters. The inordinate amount of noise helicopters produce is a major problem in the both a military and civilian setting. To remedy this problem the use of an aerogel coat…
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

824 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