Solving Inverse Function: sec(2x+180)=2, 0<x<360

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Homework Help Overview

The discussion revolves around solving the equation sec(2x + 180) = 2 within the interval 0 < x < 360 degrees. Participants are exploring the implications of transforming the equation into a cosine function.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the transformation of the secant equation into a cosine equation and the implications of the phase shift introduced by the 180-degree term. There is a question regarding the number of solutions, with some participants noting discrepancies between their findings and those in the textbook.

Discussion Status

There is an ongoing exploration of different approaches to solve the equation, with some participants suggesting alternative methods for handling the phase shift and the cosine function. Multiple interpretations of the problem are being considered, but no consensus has been reached yet.

Contextual Notes

Participants are working within the constraints of the specified interval for x and are questioning how the phase shift affects the number of solutions. There is an acknowledgment of the need to find all valid solutions within the given range.

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I can only find two answers for this equation, whereas the books says it should be four. Can someone enlighten me? Showing the procedure would help:P

(degrees)
sec(2x+180) = 2 0<x<360
 
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First write it as cos(2x+180)=1/2.

Then get rid of the 180 (the 180 causes a shift in the graph of cos(2x)).
 
Galileo said:
First write it as cos(2x+180)=1/2.

Then get rid of the 180 (the 180 causes a shift in the graph of cos(2x)).

Changing to cosine is a good idea, but you can't get rid of 180 and get the right answers for x. You could change the cosine to -cos(2x) = 1/2, or set the argument of the cosine as it stands to the values that have cosine = 1/2, then solve for x, keeping only the solutions in the specified interval.
 
OlderDan said:
You could change the cosine to -cos(2x) = 1/2
That's what I meant by 'getting rid of the 180'.
 
Check the range of x:
0 < x < 360
180 < 2x + 180 < 900
 

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