How to find a general solution

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Homework Help Overview

The discussion revolves around finding the general solution to the equation sin(3x) + sin(2x) = 0, which falls under the subject area of trigonometric equations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the use of trigonometric identities, such as the double angle identity for sine and the expression for sin(3x). There is uncertainty about how to proceed after applying these identities, and some participants express confusion regarding the "sin general solution formula."

Discussion Status

The discussion is ongoing, with participants sharing various identities and attempting to clarify their understanding of the problem. Some guidance has been offered regarding rewriting the equation in terms of sine and cosine, but there is no explicit consensus on the next steps.

Contextual Notes

Participants mention a need for a general solution formula and express uncertainty about the application of trigonometric identities, indicating potential gaps in foundational knowledge or assumptions about the problem setup.

chris99191
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1. Find the general solution to sin3x+sin2x=0


2. I am not sure what to use. I think the sin2x=2sinxcosx but I am unsure where to go from there


3. sin3x+2sinxcosx=0 unsure
 
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This still doesn't help me understand sorry. I think we have to put them into the sin general solution formula but I am not sure how
 
I have no idea what you mean by "sin general solution formula" but what the others are referring to are that
[tex]\sin(2x)= 2\sin(x)\cos(x)[/tex]
and
[tex]sin(3x)= 3\sin(x)cos^2(x)- \sin^3(x)[/tex]
[tex]= 3sin(x)(1- \sin^2(x))- \sin^3(x)= 3\sin(x)- 4\sin^3(x)[/tex]

You can write your equation in terms of sine and cosine only.
 

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