Solving for Sin(π/12): How Do I Get (π/3-π/4)?

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Discussion Overview

The discussion revolves around understanding how to express sin(π/12) using compound angle formulas, specifically relating it to the expression (π/3 - π/4). Participants are exploring the mathematical reasoning behind this relationship, focusing on the arithmetic involved in manipulating fractions.

Discussion Character

  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how π/12 can be represented as (π/3 - π/4), indicating a lack of understanding in the solution provided in their math course.
  • Another participant suggests that the issue may stem from basic arithmetic involving fractions, implying that a simpler perspective might clarify the relationship.
  • A later reply acknowledges a personal realization that the solution is straightforward when viewed from a basic arithmetic standpoint, suggesting that over-analysis can complicate understanding.
  • There is a mention of the importance of decomposing fractions and using familiar fractions to aid in understanding the angle sum or difference formulas.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the clarity of the solution, as some express confusion while others find the solution straightforward after reconsideration. The discussion reflects varying levels of understanding regarding the manipulation of angles and fractions.

Contextual Notes

The discussion highlights potential limitations in understanding the decomposition of fractions and the application of angle sum or difference formulas, without resolving these issues.

Markg1997
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In then math course I am taking it is giving the example of using compound angle formulas to solve sin(pi/12). The solution in the formula says that it is (pi/3-pi/4). I don't understand how pi/12 is equal to (pi/3-pi/4). What am I missing in this solution?
 
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Markg1997 said:
In then math course I am taking it is giving the example of using compound angle formulas to solve sin(pi/12). The solution in the formula says that it is (pi/3-pi/4). I don't understand how pi/12 is equal to (pi/3-pi/4). What am I missing in this solution?
Basic arithmetic for fractions
 
Now I feel dumb. Amazing how the simple things elude you. Once i looked at it from a basic perspective instead of trying to over analyze it was plain and simple. Thanks.
 
Markg1997 said:
Now I feel dumb. Amazing how the simple things elude you. Once i looked at it from a basic perspective instead of trying to over analyze it was plain and simple. Thanks.

Exactly what to say and how to say it seemed unapparent. You're dealing with angle sum or difference formulas, and you have fractions. Students are not accustomed to decomposing fractions this way, but really this is still elementary basic arithmetic. You usually want to play with simpler more common fractions to look for how to decompose your fraction factor of pi.
 

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