Solve Secx=-5.2 | Find Solutions for x Between 0 and 2π

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Homework Help Overview

The problem involves solving the equation sec(x) = -5.2 for values of x within the interval [0, 2π]. Participants are discussing their findings and the validity of their solutions.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants share their calculated solutions of 1.76 and 4.52, questioning the correctness of the answer key which only lists 1.76. There is a discussion about the method used to find the second solution, with references to properties of cosine.

Discussion Status

Some participants confirm the initial solution of 1.76, while others seek clarification on the method for deriving the second solution. The conversation reflects a mix of agreement and inquiry regarding the approach taken.

Contextual Notes

There is an emphasis on the constraints of the interval [0, 2π] and the nature of the secant function, which may influence the solutions discussed.

dragon513
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Q. Solve: secx=-5.2
x is greater than or equal to zero and less than or equal to 2π

I got 1.76 and 4.52, but answer key only has 1.76.

Am I not right?
 
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I find the same answers as you do when I do a quick check using my TI-89. Hmmm :confused:
 
dragon513 said:
Q. Solve: secx=-5.2
x is greater than or equal to zero and less than or equal to 2π
I got 1.76 and 4.52, but answer key only has 1.76.
Am I not right?
Yup, that looks good to me. :smile: Your answer is correct!
 
Thank you!
 
dragon513 said:
Thank you!
Once you had the first solution 1.76, how did you find the 2nd one?
 
Since you have cos(-x) = cos(x), and [itex]\cos x = \cos (x + 2k \pi) \ \ , k \in \mathbb{Z}[/itex]
So the second one is just:
[tex]- 1.76 + 2 \pi = 4.52[/tex]
 
Thanks for answering, but I was asking dragon513.
dragon513, what was your approach for finding the 2nd angle?
 

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