Trigonometry Problem

[Madhav Goel]

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

 

[mfb]

Did you draw a sketch?
I think there is some error in the problem statement.

 

[RUber]

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.

 

[HallsofIvy]

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.)