Trigonometry Algebraic problem

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The discussion revolves around solving two trigonometric equations for the variable x, specifically focusing on the equations p(x) = 5000 cos [∏/2 (x-1)] + 6000 and p(x) = 15000 cos [∏/2 (x+((∏/2)-1))] + 25000. Participants emphasize the need to equate the two equations and simplify them using cosine sum formulas. There is a debate about whether the problem is fundamentally a trigonometric equation or if it requires a more graphical approach, with one contributor suggesting the construction of a table for cosine values. The conversation highlights the importance of showing work for review, as the original poster struggles to arrive at the correct solution. The problem ultimately seeks the correct value of x through algebraic manipulation.
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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