Distributing Cos45 in an Expression: Numerator and Denominator

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Discussion Overview

The discussion revolves around the distribution of the cosine of 45 degrees in a mathematical expression involving both a numerator and a denominator. Participants explore whether cos(45) should be applied only to the numerator or if it can also be distributed to the denominator.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant suggests that cos(45) should only be multiplied into the numerator, reasoning that it can be viewed as cos(45)/1, which implies it only affects the numerator.
  • Another participant argues that if cos(45) were to be multiplied into both the numerator and the denominator, it would lead to cancellation of cos(45), which they indicate is not the desired outcome.
  • There is a mention of the value of cos(45), which some participants note is a simple value, although this is not elaborated upon in detail.

Areas of Agreement / Disagreement

Participants generally agree that cos(45) should only be applied to the numerator, but there is a lack of consensus on the implications of distributing it to the denominator.

Contextual Notes

No specific limitations or unresolved mathematical steps are noted in the discussion.

Who May Find This Useful

This discussion may be useful for individuals interested in mathematical expressions, particularly those involving trigonometric functions and their manipulation.

Ryuk1990
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Let's say I have an expression like this.

cos45[(601-148)/sin21.8]

Does cos45 get multiplied into just the numerator terms or do I also distribute it to the denominator as well?
 
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Only the numerator. Think of it as cos(45)/1 so that cos(45) multiplies the numerator and 1 multiples the denominator.

Also, notice that cos(45) equals something simple.
 
Multiplying into the numerator and the denominator would give you [tex]\frac{cos(45)(601-148)}{cos(45)sin(21.8)}[/tex] and the cosines would cancel which is not what you want.
 
Ok, thanks guys.
 

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