Trig solve for all angles x problem

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Homework Help Overview

The problem involves solving the equation Sin(x) + Sin(2x) + Sin(x) * Cos(2x) + Sin(2x) * Cos(x) = 0 for all angles x, within the context of trigonometric identities and equations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to approach the problem, considering factoring out Sin(x) as a potential step. Other participants discuss the use of double angle identities to simplify the equation and mention the application of the cos^2 identity.

Discussion Status

The discussion includes attempts to simplify the equation using trigonometric identities, with some participants sharing their methods and others expressing their understanding of the approach. There is a sense of progress as one participant indicates they feel they have grasped the concept after the exchange.

Contextual Notes

Participants mention constraints such as the inability to share visual aids like scanned papers, which may limit the depth of explanation in the discussion.

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Homework Statement


Sin(x)+sin(2x)+sin(x)*Cos(2x)+sin(2x)*cos(x)=0
Solve for all angles x.

Homework Equations


Sin(2x)= 2sin(x)*cos(x)

The Attempt at a Solution


Not really sure what to do. I noticed that i could maybe factor out Sin(x), but i do not really know if that is right.

I seem to be always stuck on these kind of problems. Any general tips would greatly help me as well. Thank you
 
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Last edited by a moderator:
So you just used double angles to get rid of sin(2x) and cos(2x)?
 
Yes I used double angles for them and I had to use the cos^2 identity also. I wish I could just scan my paper and upload it but no scanner.
 
Cool, i think i got it now. Thanks for your time.
 

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