Solving Simple Trig Identities Homework Problem

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Homework Help Overview

The discussion revolves around simplifying a trigonometric expression involving sine and cosine functions, specifically f(t) = sin(βt) * cos(βt). Participants are exploring trigonometric identities and simplification techniques.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to simplify the expression using trigonometric identities but encounters difficulties. Some participants question the variable used in the expression, while others suggest using known identities like 2sin(x)cos(x) = sin(2x) to aid in simplification.

Discussion Status

Participants are actively engaging with the problem, with some providing insights into potential identities that could be useful. There is a recognition of the need for clarification regarding the variable in the expression, and a productive direction is emerging with the mention of relevant identities.

Contextual Notes

There is a noted confusion regarding the variable in the expression, initially referred to as f(x) before being corrected to f(t). This may affect the interpretation of the problem.

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Homework Statement



Simplify this expression:
f(t) = sin([tex]\beta[/tex]t)*cos([tex]\beta[/tex]t)

Homework Equations



Identities

The Attempt at a Solution



I started out by doing sin([tex]\beta[/tex]t)*sin([tex]\beta[/tex]t+[tex]\pi[/tex]/2) but I can't go anywhere from there. If I use the sin(a+b) formula it brings me back to the original formula which it should. Anyone have an idea? Just the start would be MUCH appreciated.
 
Last edited:
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You have f(x) but no x anywhere on the other side. What is the variable and what is constant?
 
Sorry about that. It should be f(t).
 
The first thing that came to mind was 2sinxcosx = sin2x
 
Ahh! I think that is what I needed. If 2sin(x)cos(x)=sin(2x) then I can multiply both sides by 2 which gives 2f(t)=2sin([tex]\beta[/tex]t)cos([tex]\beta[/tex]t). After, just carry the 2 over so you get f(t)=(1/2)sin(2[tex]\beta[/tex]t). Thanks man!
 

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