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

In summary, the problem is to solve for x in the equation 2sinx = 3x^2 + 2x + 3. The relevant equation to find the lowest value of the quadratic function is -D/4a (where D is the discriminant). The range of 2sinx is inconsistent with the given polynomial equation. This type of problem, with a transcendental function equal to a polynomial, requires a numerical method to solve. Using the Lambert's W function is also a possibility, but it may introduce complex numbers in the process.

## 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

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.)

## What is trigonometry?

Trigonometry is a branch of mathematics that deals with the study of triangles and their relationships between angles and sides. It is used to solve problems involving triangles, circles, and periodic phenomena.

## What is the given problem, 2sinx= 3x2 + 2x + 3, asking to solve?

The given problem is asking to find the value(s) of x that satisfy the equation 2sinx= 3x2 + 2x + 3. This can be done by using trigonometric identities and solving for x.

## What are some common strategies for solving trigonometry problems?

Some common strategies for solving trigonometry problems include using trigonometric identities, converting between different forms of trigonometric functions, and using the unit circle. It is also important to understand the properties and relationships of triangles and angles in order to effectively solve problems.

## How can the given problem be solved using trigonometric identities?

The given problem can be solved by using the fact that sinx can be rewritten as (1/2)(2sinx). By substituting this into the equation, we get (1/2)(2sinx) = 3x2 + 2x + 3. Then, we can use the double angle identity for sine to rewrite the equation as sin2x = 3x2 + 2x + 3. From there, we can use algebraic techniques to solve for x.

## Can the solution to the given problem be verified?

Yes, the solution to the given problem can be verified by substituting the value(s) of x into the original equation and checking if it satisfies the equation. Additionally, graphing the equation and the solution can also serve as a visual verification of the solution.