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

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SUMMARY

The equation 2sin(x) = 3x² + 2x + 3 presents a transcendental function equated to a polynomial, making it complex to solve analytically. The lowest value of the quadratic function can be determined using the formula -D/4a, where D is the discriminant. Due to the nature of the functions involved, numerical methods are necessary for finding solutions. The Lambert W function is a potential tool for solving such equations, but it introduces complexities with exponential conversions.

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  • Understanding of transcendental equations
  • Familiarity with quadratic functions and discriminants
  • Knowledge of numerical methods for solving equations
  • Basic concepts of the Lambert W function
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  • Learn about the properties and applications of the Lambert W function
  • Study the discriminant and its role in determining the nature of quadratic functions
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Students studying mathematics, particularly those tackling advanced algebra and trigonometry, as well as educators seeking to explain complex equation-solving techniques.

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 xe^x but converting sine to exponentials will introduce complex numbers so I would not be inclined to try that.)
 

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