Some number belongs to real such that

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Homework Help Overview

The problem involves finding a real number x that satisfies the equation sin(x) = x - 1. The discussion centers around the properties of the sine function and the linear function represented by x - 1.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the sine function and the linear equation, with one participant attempting to establish intervals based on the properties of sin(x). Others suggest graphical methods and question the existence of a solution within certain bounds.

Discussion Status

The discussion is ongoing, with some participants affirming the existence of a solution while others express skepticism about the specific bounds proposed. There is no explicit consensus on the existence of a solution, but various approaches are being considered.

Contextual Notes

Participants are working within the constraints of the sine function's range and the linear equation's behavior, questioning the assumptions made about the intervals and the existence of solutions.

lovemake1
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Homework Statement



sin(x) = x - 1

Homework Equations





The Attempt at a Solution



i used the fact that -1 < sin(x) < 1
and set interval to [0, 2pi].

this gave me,

-1 < sin(x) < 1 and -1 < x - 1 < 2pi - 1
so therefore, since sin(x) < 1 < 2pi - 1
there must be x, real number that lies between -1 and 1.


is this correct?
 
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Draw a graph of y=sin(x) versus y=x-1.
 
You are correct in proving that such a x exists. Do you also need to find that x? That seems a bit difficult...
 
There is no such x between -1 and 1. That is not to say that such an x does not exist.
 

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