Trigonometry Algebraic problem

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Homework Help Overview

The discussion revolves around a trigonometric algebraic problem involving two equations defined by cosine functions. The original poster seeks assistance in solving for the variable x, noting that there are two solutions that appear periodically. The equations provided are p(x) = 5000 cos [∏/2 (x-1)] + 6000 and p(x) = 15000 cos [∏/2 (x+((∏/2)-1))] + 25000, with a request for algebraic methods rather than graphical solutions.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants question the specific requirements of the problem, particularly whether it asks for the value of x and if the two functions are distinct. There are suggestions to equate the two equations and simplify, with references to using cosine sum formulas. Some participants express uncertainty about the nature of the problem, debating whether it is a trigonometric equation or more about understanding the properties of cosine graphs.

Discussion Status

The discussion is ongoing, with various interpretations of the problem being explored. Some participants have offered guidance on equating the functions and simplifying, while others emphasize the need for the original poster to show their work for further examination. There is no explicit consensus on the approach to take, and multiple lines of reasoning are being considered.

Contextual Notes

Participants note the requirement to solve the problem without a graphing calculator and the original poster's mention of having received an incorrect solution. There is also a discussion about the periodic nature of the solutions and the implications of the cosine functions' properties.

hunter45
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Hello,

Could you please help me with a problem that I saw in my exam? I have tried to solve it but end up getting one solution which is not correct. There happens to be 2 solutions to the problem which appear periodically.

The problem has to be algebraically solved without the use of a graphing calculator so I would appreciate if working is given.

Equation 1: p(x) = 5000 cos [∏/2 (x-1)] + 6000
Equation 2: p(x) = 15000 cos [∏/2 (x+((∏/2)-1))] + 25000

Thanks in advance.
 
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What does the problem ask for? The value of x? And are the functions in eqn 1 and 2 different? You denoted one of them by p and the other one by P.
 
Millennial said:
What does the problem ask for? The value of x? And are the functions in eqn 1 and 2 different? You denoted one of them by p and the other one by P.

Yes, solve for x. All I know is that you must equate them. I do not know where to go from there.
 
Equate them and do the necessary simplifications, then use the cosine sum formulae to expand the cosines.
 
Millennial said:
Equate them and do the necessary simplifications, then use the cosine sum formulae to expand the cosines.

Thats what I did but the answer is still incorrect. Could you please work it out so I can see how to do it correct.
 
No, at PF, it is the policy for you to show your work. We will examine it and note any flaws in your reasoning and/or calculations.
 
I don't think that this is a trigonometric equation so to speak in the sense of solving for x, what it looks like to me is a Cosine graph in which the vertical shift is +6000, the amplitude is 5000 and the period for cosine is "2pi over b". "b" in this case is "Pi over 2." "2Pi" divided by "Pi over 2" is 4. So that is your period for this cosine graph. This problem requires you to make a table which is almost impossible for me to describe in words but basically the top row would be 0, pi/2, pi, 3pi/2, and 2pi. I'm sorry this reads confusing because I don't know where the Pi button is yet. In trigonometry pi over 2 also refers to 90 degrees and pi refers to 180 degrees.
 

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