Simplify with Trigonometric Identities

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Homework Help Overview

The discussion revolves around simplifying trigonometric expressions related to a physics problem involving a rod with two masses spinning in a circle. Participants are exploring various trigonometric identities to aid in the simplification process.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to simplify expressions using trigonometric identities but expresses difficulty in applying them correctly, particularly due to the presence of different angles. Some participants suggest using the identity sin²x + cos²x = 1, while others propose factoring common terms.

Discussion Status

Participants are actively engaging with the problem, offering guidance on potential approaches, such as applying specific identities and factoring common factors. There is a recognition of the complexity due to multiple angles involved, and the discussion is ongoing without a clear consensus.

Contextual Notes

The original poster has provided their work and a simplified version they believe to be the answer, indicating that there may be constraints or specific requirements related to the homework assignment.

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Homework Statement




I'm trying to simplify some trigonometric expressions, I'm attaching my work here. This comes from a famous physics problem i.e. the rod with two masses spinning on a circle. I've tried many times but I just can't get it. Any help on which identities to use would really help me.



Homework Equations



I'm attaching the simplified version, the 'answer'


The Attempt at a Solution



I'm attaching my work.
 

Attachments

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  • Screen Shot 2014-09-06 at 2.12.59 AM.png
    Screen Shot 2014-09-06 at 2.12.59 AM.png
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Apply a couple of times sin2 x + cos2 x = 1
and your last line simplifies to the given answer
 
NascentOxygen said:
Apply a couple of times sin2 x + cos2 x = 1
and your last line simplifies to the given answer

Yes, I looked at that identity, but there are 2 different angles in this problem, and also one of my last two terms is dø2*sin2Θ

Any direction on how to first apply the identity would also help?
 
Take cos2 θ outside some brackets because it's a common factor.

And you'll see again, there's another common factor in two other terms to treat similarly.
 

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