MHB Need Help With a Trigonometric Equation?

AI Thread Summary
The discussion revolves around solving a trigonometric equation where the user is seeking assistance after getting stuck. It is confirmed that the solution provided is valid, with the cosine function repeating every 2π/3, indicating no additional solutions exist within the specified domain. The user questions whether their solution for x is complete or if it can be further simplified. Responses suggest that the solution fits within the restricted domain and that while combining fractions is possible, the current form is acceptable. Overall, the conversation emphasizes confirming the validity of the solution and understanding the periodic nature of the trigonometric function involved.
siyanor
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can somebody help me out on this one,i got stuck on this one
https://www.physicsforums.com/attachments/164
 

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Re: Trigonometry

siyanor said:
can somebody help me out on this one,i got stuck on this one
https://www.physicsforums.com/attachments/164

That's a valid solution.

cos(3x-1) repeats every 2pi/3 so there won't be any more solutions in the domain given.
 
Re: Trigonometry

but how we are going to find the value of x ?(is my solution complete or it could go further than this?
 
Re: Trigonometry

siyanor said:
but how we are going to find the value of x ?(is my solution complete or it could go further than this?

You solved for x and it fits within the restricted domain the problem stated. You could combine the fractions but I think it's fine as it is.
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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