Solve Trigonometry Problem: 2sinx= 3x2 + 2x + 3

  • Thread starter Thread starter Madhav Goel
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Homework Help Overview

The problem involves solving the equation 2sin(x) = 3x² + 2x + 3, which combines a trigonometric function with a polynomial expression. The discussion centers on the nature of the equation and the methods that may be applicable for finding solutions.

Discussion Character

  • Exploratory, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants express uncertainty about how to approach the problem, with one noting a potential error in the problem statement. Others question the relationship between the quadratic function's lowest value and the range of the sine function, suggesting possible inconsistencies.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the equation. Some have suggested that numerical methods may be necessary for solving the equation, while others are examining the implications of the functions involved.

Contextual Notes

There are indications that the problem may contain errors or inconsistencies, particularly regarding the relationship between the trigonometric and polynomial components. Participants are also considering the implications of using complex numbers in their reasoning.

Madhav Goel
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Homework Statement


Solve for x
2sinx= 3x2 + 2x + 3[/B]

Homework Equations


Lowest value of quadratic function = -D/4a (D= Discriminant)

The Attempt at a Solution


I have no idea how to do it
 
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Did you draw a sketch?
I think there is some error in the problem statement.
 
Based on your entry for #2, relevant equations, what do you know about the lowest value of the quadratic function? What is the range of 2sinx? As to mfb's point, these may be inconsistent.
 
This equation has a transcendental function equal to a polynomial. In general, there is no simple way to solve such problems. You will need to use a numerical method. (Such equations can be solved using "Lambert's W function" which is defined as the inverse function to [itex]xe^x[/itex] but converting sine to exponentials will introduce complex numbers so I would not be inclined to try that.)
 

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